{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# **Concepts Covered:**\n", "\n", "- Central Limit Theorem (CLT)\n", "- Point Estimation\n", "- Confidence Interval\n", "- Hypothesis Test for Population Mean $\\mu$\n", "- One-tailed and Two-tailed Tests" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import the required packages" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "id": "n1269wHJF96t" }, "outputs": [], "source": [ "#import the important packages\n", "import pandas as pd #library used for data manipulation and analysis\n", "import numpy as np # library used for working with arrays.\n", "import matplotlib.pyplot as plt # library for plots and visualisations\n", "import seaborn as sns # library for visualisations\n", "%matplotlib inline \n", "\n", "import scipy.stats as stats # this library contains a large number of probability distributions as well as a growing library of statistical functions." ] }, { "cell_type": "markdown", "metadata": { "id": "26wT4S4S5yrm" }, "source": [ "# **Central Limit Theorem (CLT)**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Central Limit Theorem states that if we independently draw multiple samples from a population, take the mean of each sample and plot these (sample means), then the plot will tend to normal distribution as the size of samples increases, **regardless** of the shape of the population distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Let's watch CLT in action using a python simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Here is a Uniform Distribution (which is most definitely *not Normal*)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# importing the required function\n", "from scipy.stats import uniform\n", "\n", "# setting the seed for reproducibility\n", "np.random.seed(1)\n", "# creating a uniform distribution population of size 100000\n", "uniform_pop = uniform.rvs(0, 10, size=100000)\n", "# visualizing the uniform distribution\n", "plt.hist(uniform_pop)\n", "plt.title(\"Uniform Distribution Population\")\n", "plt.xlabel(\"X~U(0,10)\")\n", "plt.ylabel(\"Count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Let's create a sampling distribution from this population (sample size=5, number of samples = 500)\n", "\n", "* draw a sample of size 5, so n=5, we draw 5 independent observations\n", "* get the mean of these 5 observations, i.e - sample mean\n", "* repeat the above 2 steps 500 times, so that we get 500 sample means, where n=5 \n", "\n", "Now, let's observe the shape of this sampling distribution." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 5\n", "n = 5\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(uniform_pop, size=n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde=True)\n", "plt.title(\"Distribution of Sample Means for n = \" + str(n))\n", "plt.xlabel(\"sample mean\")\n", "plt.ylabel(\"count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Let's create another sampling distribution from this population, increase the sample size to 15 (n=15)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 15\n", "n = 15\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(uniform_pop, size=n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde=True)\n", "plt.title(\"Distribution of Sample Means for n = \" + str(n))\n", "plt.xlabel(\"sample mean\")\n", "plt.ylabel(\"count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Increase the sample size to 30 (n=30)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 30\n", "n = 30\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(uniform_pop, size=n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde=True)\n", "plt.title(\"Distribution of Sample Means for n = \" + str(n))\n", "plt.xlabel(\"sample mean\")\n", "plt.ylabel(\"count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Increase the sample size to 50 (n=50)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 50\n", "n = 50\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(uniform_pop, size=n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde=True)\n", "plt.title(\"Distribution of Sample Means for n = \" + str(n))\n", "plt.xlabel(\"sample mean\")\n", "plt.ylabel(\"count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Insight\n", "\n", "* Observe how the sampling distribution moves closer to normality as the sample size increases." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### When the population distribution is Normal" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# import the required function\n", "from scipy.stats import norm\n", "\n", "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# create a normal distribution population of size 100000\n", "normal_pop = norm.rvs(0, 1, size=100000)\n", "# visualize the normal distribution\n", "plt.hist(normal_pop, 200)\n", "plt.title(\"Normal Distribution Population\")\n", "plt.xlabel(\"X~N(0,1)\")\n", "plt.ylabel(\"Count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Let's create a sampling distribution from this population (sample size=5, number of samples = 500)\n", "\n", "* draw a sample of size 5, so n=5, we draw 5 independent observations\n", "* get the mean of these 5 observations, i.e - sample mean\n", "* repeat the above 2 steps 500 times, so that we get 500 sample means, where n=5 \n", "\n", "Now, let's observe the shape of this sampling distribution." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 5\n", "n = 5\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(normal_pop, size = n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde = True)\n", "plt.title('Distribution of Sample Means for n = ' + str(n))\n", "plt.xlabel('sample mean')\n", "plt.ylabel('count')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Insight\n", "\n", "* When the population distribution is Normal, sampling distribution is close to normal for even the smaller sampling sizes like n = 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Let's check sampling distribution for sample size n = 15" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 15\n", "n = 15\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(normal_pop, size=n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde=True)\n", "plt.title(\"Distribution of Sample Means for n = \" + str(n))\n", "plt.xlabel(\"sample mean\")\n", "plt.ylabel(\"count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sampling Distribution when Sample Size n = 30\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 30\n", "n = 30\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(normal_pop, size=n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde=True)\n", "plt.title(\"Distribution of Sample Means for n = \" + str(n))\n", "plt.xlabel(\"sample mean\")\n", "plt.ylabel(\"count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Let's see if CLT works if the population distribution is Exponential Distribution (which again is clearly *not Normal*)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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vHBxmZlaIg8PMzApxcJiZWSEODjMzK8TBYWZmhTg4zMysEAdHFTRNnefTcs2s33BwmJlZIQ4OMzMrxMFhZmaFODjMzKwQB4eZmRXi4DAzs0IqCg5JR1ZSZmZmfV+lPY4fVFhmZmZ93MCOXpR0BPBhYKikL+ZeGgwMqGXDzMysd+owOIDtgZ3Tcrvkyl8G/rpWjTIzs96rw+CIiIeAhyTNioine6hNDatp6jxWTz+x3s0wM6upznocJYMkzQSa8nUi4mO1aJSZmfVelQbHT4EfAdcBb9WuOWZm1ttVGhxbImJGTVvSR5TukushKzPrqyo9HfcuSX8nabikIaVHTVtmZma9UqXBMQn4EvBLYEl6tHRUQdIOkhZLekzSMknfSOVDJC2QtDI9756rM03SKkkrJB2fKz9M0tL02jWSVHRHzcysOioKjogYU+axdyfVXgc+FhEHA4cA4yWNA6YCCyNiLLAwzSPpAGACcCAwHrhWUulakRnAFGBseowvspNmZlY9FR3jkDSxXHlE3NhenYgI4JU0u116BHAKcHQqnw08CHw5ld8WEa8DT0laBRwuaTUwOCIWpbbcCJwKzK+k7WZmVl2VHhz/YG56B+BY4FGg3eAASD2GJcA+wD9HxMOShkXEeoCIWC9pz7T4COBXueqtqezNNN22vNz2ppD1TBg9enRle2ZmZoVUFBwRcX5+XtKuwE0V1HsLOETSbsAdkg7qYPFyxy2ig/Jy25sJzARobm4uu4yZmXVPV2+r/hrZsYaKRMSLZENS44ENkoYDpOeNabFWYFSu2khgXSofWabczMzqoNLbqt8laW56zANWAHd2Umdo6mkgaUfg48DvgLlkZ2mRnkvrmQtMkDRI0hiyYFqchrU2SxqXzqaa2Nm2zcysdio9xvG93PQW4OmIaG1v4WQ4MDsd53gPMCci7pa0CJgjaTKwBjgNICKWSZoDPJG2cV4a6gI4F5gF7Eh2ULzXHxj3favMrK+q9BjHQ5KGsfUg+coK6vwWOLRM+XNkB9fL1bkcuLxMeQvQ0fERMzPrIZUOVZ0OLCbrHZwOPCzJt1U3M+uHKh2quhT4YERshOz4BfCfwO21apiZmfVOlZ5V9Z5SaCTPFahrZmZ9SKU9jnsk3QvcmubPAP6jNk0yM7PerLPfHN8HGBYRX5L0KeAosgvyFgG39ED7GppvsW5mfVFnw01XAZsBIuJnEfHFiLiIrLdxVW2bZmZmvVFnwdGUTqt9l3R6bFNNWtQHlXoeZmZ9QWfBsUMHr+1YzYaYmVlj6Cw4HpH02baF6arvJbVpkpmZ9WadnVV1Idldbc9ka1A0A9sDf1XDdpmZWS/VYXBExAbgw5KOYestP+ZFxP01b5mZmfVKld6r6gHggRq3pU/zqblm1lf46m8zMyvEwWFmZoU4OMzMrBAHh5mZFeLg6GG+itzMGp2Dw8zMCnFwmJlZIQ4OMzMrxMFhZmaFODjMzKwQB0cdNE2d57OrzKxhOTjMzKwQB4eZmRXi4DAzs0IcHGZmVkjNgkPSKEkPSFouaZmkC1L5EEkLJK1Mz7vn6kyTtErSCknH58oPk7Q0vXaNJNWq3WZm1rFa9ji2ABdHxP7AOOA8SQcAU4GFETEWWJjmSa9NAA4ExgPXShqQ1jUDmAKMTY/xNWx3j/GZVWbWiGoWHBGxPiIeTdObgeXACOAUYHZabDZwapo+BbgtIl6PiKeAVcDhkoYDgyNiUUQEcGOujpmZ9bAeOcYhqQk4FHgYGBYR6yELF2DPtNgIYG2uWmsqG5Gm25aX284USS2SWjZt2lTVfagVX9NhZo2m5sEhaWfg34ELI+LljhYtUxYdlG9bGDEzIpojonno0KHFG2tmZp2qaXBI2o4sNG6JiJ+l4g1p+In0vDGVtwKjctVHAutS+cgy5WZmVge1PKtKwPXA8oi4MvfSXGBSmp4E3JkrnyBpkKQxZAfBF6fhrM2SxqV1TszVMTOzHjawhus+EjgbWCrpN6nsK8B0YI6kycAa4DSAiFgmaQ7wBNkZWedFxFup3rnALGBHYH56mJlZHSg7UanvaW5ujpaWli7VrdfB6tXTT6zLds3MSiQtiYjmjpbxleNmZlaIg8PMzApxcPQivqbDzBqBg8PMzApxcJiZWSEODjMzK8TBYWZmhTg4zMysEAdHL+Qzq8ysN3NwmJlZIQ6OXsrXdJhZb+Xg6OUcHmbW2zg4zMysEAeHmZkV4uAwM7NCHBxmZlaIg8PMzApxcJiZWSEOjgbgazrMrDdxcDQQh4eZ9QYODjMzK8TBYWZmhQysdwOsmLbDVaunn1inlphZf+Ueh5mZFeLgMDOzQhwcZmZWiIPDzMwKqVlwSLpB0kZJj+fKhkhaIGllet4999o0SaskrZB0fK78MElL02vXSFKt2tyIfG2HmfW0WvY4ZgHj25RNBRZGxFhgYZpH0gHABODAVOdaSQNSnRnAFGBserRdp5mZ9aCaBUdE/Bx4vk3xKcDsND0bODVXfltEvB4RTwGrgMMlDQcGR8SiiAjgxlwdS3xLEjPrST19jGNYRKwHSM97pvIRwNrccq2pbESabltuZmZ10lsOjpc7bhEdlJdfiTRFUouklk2bNlWtcWZmtlVPB8eGNPxEet6YyluBUbnlRgLrUvnIMuVlRcTMiGiOiOahQ4dWteGNwMNVZtYTejo45gKT0vQk4M5c+QRJgySNITsIvjgNZ22WNC6dTTUxV8fMzOqglqfj3gosAvaV1CppMjAdOE7SSuC4NE9ELAPmAE8A9wDnRcRbaVXnAteRHTD/b2B+rdrcl7j3YWa1UrObHEbEp9t56dh2lr8cuLxMeQtwUBWb1qc5MMys1nrLwXEzM2sQDg4zMyvEv8fRh+WHrfy7HWZWLe5xmJlZIe5x9BPufZhZtbjHYWZmhTg4zMysEAdHP+ZrPsysK3yMox9yYJhZd7jHYYDDxMwq5x5HP+fAMLOi3OMwM7NCHBz2Dv8ErZlVwkNVtg1fLGhmHXGPw8zMCnFwWIfyvQ8PY5kZeKjKKlAuPDyEZdZ/ucdhZmaFuMdhXeID6Gb9l3scVjU+BmLWP7jHYd3mYyBm/Yt7HGZmVoh7HFYTbY+BuCdi1ne4x2E152tBzPoW9zisx/mMLLPG5uCwuioXIg4Ws97NwWG9RnvDWPnjIz5WYlZ/ioh6t6Emmpubo6WlpUt1PQ7fuBwoZt0jaUlENHe0TMP0OCSNB64GBgDXRcT0OjfJeqH2Qj8fKO61mHVPQwSHpAHAPwPHAa3AI5LmRsQT9W2ZNYpygVJpz9IBY/ZuDREcwOHAqoh4EkDSbcApgIPDaq7eQ5f5kwbKnUBQblmzWmqU4BgBrM3NtwIfaruQpCnAlDT7iqQVXdzeHsCzXazbW/W1fepr+wPt7JO+XX66nM5er4N+83dqYG33Z6/OKjRKcKhM2TZH9SNiJjCz2xuTWjo7ONRo+to+9bX9Ae9To+hr+9SV/WmUK8dbgVG5+ZHAujq1xcysX2uU4HgEGCtpjKTtgQnA3Dq3ycysX2qIoaqI2CLp88C9ZKfj3hARy2q4yW4Pd/VCfW2f+tr+gPepUfS1fSq8P332AkAzM6uNRhmqMjOzXsLBYWZmhTg4ciSNl7RC0ipJU+vdnu6SNErSA5KWS1om6YJ6t6laJA2Q9GtJd9e7LdUgaTdJt0v6Xfp7HVHvNnWHpIvSv7nHJd0qaYd6t6koSTdI2ijp8VzZEEkLJK1Mz7vXs41FtbNP303/7n4r6Q5Ju3W2HgdHkrutyQnAAcCnJR1Q31Z12xbg4ojYHxgHnNcH9qnkAmB5vRtRRVcD90TEfsDBNPC+SRoBfAFojoiDyE5omVDfVnXJLGB8m7KpwMKIGAssTPONZBbb7tMC4KCI+HPg98C0zlbi4NjqnduaRMQbQOm2Jg0rItZHxKNpejPZh9GI+raq+ySNBE4Erqt3W6pB0mDgfwHXA0TEGxHxYl0b1X0DgR0lDQR2ogGvu4qInwPPtyk+BZidpmcDp/Zkm7qr3D5FxH0RsSXN/orsOrkOOTi2Kndbk4b/kC2R1AQcCjxc56ZUw1XAJcDbdW5HtewNbAL+NQ2/XSfpvfVuVFdFxB+A7wFrgPXASxFxX31bVTXDImI9ZF/MgD3r3J5qOweY39lCDo6tKrqtSSOStDPw78CFEfFyvdvTHZJOAjZGxJJ6t6WKBgJ/AcyIiEOBV2m8IZB3pHH/U4AxwPuB90o6q76tss5IupRsePuWzpZ1cGzVJ29rImk7stC4JSJ+Vu/2VMGRwMmSVpMNJ35M0s31bVK3tQKtEVHqDd5OFiSN6uPAUxGxKSLeBH4GfLjObaqWDZKGA6TnjXVuT1VImgScBJwZFVzc5+DYqs/d1kSSyMbNl0fElfVuTzVExLSIGBkRTWR/o/sjoqG/zUbEM8BaSfumomNp7J8MWAOMk7RT+jd4LA18sL+NucCkND0JuLOObamK9CN5XwZOjojXKqnj4EjSwaHSbU2WA3NqfFuTnnAkcDbZt/LfpMcn6t0oK+t84BZJvwUOAf6pvs3putRzuh14FFhK9jnTcLfpkHQrsAjYV1KrpMnAdOA4SSvJfliuoX6JtJ19+iGwC7AgfUb8qNP1+JYjZmZWhHscZmZWiIPDzMwKcXCYmVkhDg4zMyvEwWFmZoU4OMzKSHcWfkrSkDS/e5rfq4K6qyUtzZ0CfU032nGhpIlp+rR0x9m3JTXnlvkzSbO6ug2zohrip2PNelpErJU0g+w8/SnpeWZEPF3hKo6JiGe704Z0g8Bz2HoV+ePAp4Aft2nrUkkjJY2OiDXd2aZZJdzjMGvf98mugL4QOAq4oqsrkjRQ0iOSjk7z35J0eZpeLenbkhanxz6p2seAR0t3Lo2I5RGxop1N3EVj3rrcGpCDw6wd6T5LXyILkAsj4o0UAF+T1CLpvjR8tJ+kKySNzlV/IDdUdVH68P8MMEPScWS/ifCN3PIvR8ThZFfxXpXKjgQqvZljC/CRLu+sWQEeqjLr2AlktwY/iOwHb94PvAB8EGgGLgX2AX7cZphom6GqiFgm6Say3sER6XdfSm7NPX8/TQ+n8ns8bUxtM6s5B4dZOyQdQnY/onHAf0m6LYXDD9Iij1D8h3z+DHgRGNamPMpM/xGo9CdXd0jLm9Wch6rMykh3dZ1BNkS1Bvgu2Y8TdWednwL+hOzX/q5p89vOZ+SeF6Xp5WS9mUr8KdnBc7Oac3CYlfdZYE1ELEjz1wL7SfpohfXzxzhulLQH2ZlZkyPi92THMq7OLT9I0sNkv6V+USqbTxYyAEj6K0mtwBHAPEn35uofA8wruI9mXeK745rVWfpRquZyp+9KugO4JCJWdlB/EPAQcFTut6PNasY9DrPebSrZQfKOjAamOjSsp7jHYWZmhbjHYWZmhTg4zMysEAeHmZkV4uAwM7NCHBxmZlbI/wcyBq3WcB2mOQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# import the required function\n", "from scipy.stats import expon\n", "\n", "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# create a exponential distribution population of size 100000\n", "exp_pop = expon.rvs(size=100000)\n", "# visualize the exponential distribution\n", "plt.hist(exp_pop, 200)\n", "plt.title(\"Exponential Distribution Population\")\n", "plt.xlabel(\"X~Exp(1)\")\n", "plt.ylabel(\"Count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sampling Distribution for Sample Size n = 5" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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AqnoUqBWR0US4DNgNPAascx5bB6x3q4ZY1djVT1VLL6vKc0lKcHc/6o1nlfPQJ8/FJ8LN//0y//T73fQPjbi6TmPihdtHwt0OPCAiScAh4KMEQ//XIvJxoAa4weUaYs72mnYS/cLKsuywrG9VRS5/+uyF3PWnN/jJxsP8+Y1jfPP65Vy4sDAs6zcmVrkawKq6A1gzwVOXubneWNYzMMy+Y12cPjub5MSZHzQxKfGdsC85pWIFQ1d9hg/d20vP7g20/vnHBHraQ1+HMXHA5oKIMq/XdRBQWFme484KNHDS/ufhkQBbqtvYIu8gd8WlnD8/n+Wzs/nCVUvcqcmYGGUBHEUCAWVXfSeV+Wnkpnk3eU6C38e58/JZXJLJs2808uzeJnY3dJJYNM+zmoyJRjYXRBSpbu2le2CY5bPC0/d7MrlpSbx31WyuWlZMZ98wpev+L8/vb2IkEFeDVoyZMQvgKLKzroPURD9zC9K9LuU4EWFJSRYfPq+S7teeYltNO7/eUktn/5DXpRkT8SyAo0TPwDCHW3pYWpqF3xeaAy5CKSXRT+uTP+DaFaW09w7x0OZajnX2e12WMRHNAjhK7G/sRhVOK830upQTml+YwY1rykjwCQ9vq6O+vc/rkoyJWBbAUeKNo50UZiRHxXnc8jOSef+ZZaQl+Vm/o56mrgGvSzImIlkAR4G23kGOdQ6wuCSyW79jZaYk8r7Vs0lK8LH+1Tq6+4e9LsmYiGMBHAX2He0CYHFx9AQwBEP4ujNmMTgc4E87GwjY6Ahj3sICOAocaOqmNDuFjJToG7ZdkJHMpUuKqO/o5+XDLV6XY0xEsQCOcO29gzR3D7KgKMPrUmZsSUkWS0uz2FLdZiMjjBnDAjjCHWzqAYKjC6LZRQsLSEv08z97jtmBGsY4LIAj3MGmbgozk8lOTfS6lFOSnOjn4sWFNHcPsrPezjdnDFgAR7SegWEaOvpZEOWt31ELCjOYnZPKK4daGRi2OYWNsQCOYAebugGYXxg5hx6fChHhwoUF9A2NsLW6zetyjPGcBXAEO9DUTW5aInnp3s18FmrFWSksLMrg1doOO7OGiXsWwBGqf2iEI219zC/MCNnJNiPF2XPzGBwJsL223etSjPGUBXCEqmrpQTX6Rz9MpCAjmfmF6eyobWdw2E55b+KXBXCEqmruJTXRT3FW5M/9MBNnVuYyOBxgz9FOr0sxxjMWwJFIfFS39lCZnxZz3Q+jSrJSKM5KZkdtO6o2LtjEJwvgCJRUsoD+oQBz8mNj9MNERIQzynNo7x2iurXX63KM8YQFcARKnbcGASry07wuxVULizJJTfSzs84OzDDxyQI4AqXOW0NxVgqpbpx2PoL4fcJppZkcbu6hZ8CmqzTxxwI4wrR0D5BUuoA5Md76HbVsVjYBxXbGmbhkARxhntvfhIiPORF04k035aUnUZqdwp76Lq9LMSbsLIAjzLNvNDHS00ZRZmwOP5vIaSVZtPYOklg0z+tSjAkrC+AIMhJQnt/fRN/h7TE7/GwiC4sz8AlkLHuH16UYE1YWwBFkd30nbb1D9B/e5nUpYZWS6GdOfjppp11kcwWbuGIBHEE2HmwGoL/6VY8rCb/FJZkkZOazparV61KMCRsL4Aiy8UAzC4syGOmJv6ka5+Sno8ODPLnrmNelGBM2FsARYmB4hM1VrZy/oMDrUjyRlOCjr2oHT+46aocmm7hhARwhtte00z8UYO38fK9L8Uzvvpeoa+9jV72NCTbxwQI4Qrx4sAWfwDnz4jeA+w68gk/gyV1HvS7FmLCwAI4QLx5o5vTZ2VF/8s1TEejr5Oy5eRbAJm5YAEeAnoFhdtS2szZO+3/HumpZCfuOdXPIOR+eMbHMAjgCbDrcynBAOX++BfCVy0oAbDSEiQuuBrCIVInI6yKyQ0S2OI/licjTIrLfuc51s4ZosPFAM0kJPtbMifuPgtk5qawoy7ZuCBMXwtECfoeqnqGqa5z7dwLPqOpC4BnnflzbeLCFMytySYnx6Sen6vLTinn1SDst3QNel2KMq7zogrgOuN+5fT9wvQc1RIzWnkH2NHRy/oL4Hf0w3iWLC1GF5/c3e12KMa5yO4AVeEpEtorIbc5jxaraAOBcF7lcQ0R76WALgO2AG2P5rGzy0pP4y74mr0sxxlUJLi//fFWtF5Ei4GkReWOqb3QC+zaAiooKt+rz3MaDzWQkJ7BidrbXpUQMn0+4aGEBz+1rIhBQfL74mRnOxBdXW8CqWu9cNwKPAGcDx0SkFMC5bpzkvfeo6hpVXVNYWOhmmZ568UAz58zNI8FvA1LGunhxIS09g+yst/PFmdjl2m+9iKSLSObobeBKYCfwGLDOedk6YL1bNUS6uvY+qlp6rfthAhctLEQE/rLXuiFM7HKz2VUMvCAirwKbgD+q6hPAXcAVIrIfuMK5H5deORTs/z0vjg8/nkx+RjKnz85mg/UDmxjmWh+wqh4CVk7weAtwmVvrjSabDreSlZLAkpJMr0uJSBcvKuQHzx6go3eI7LT4PUTbxC7rePTQpsOtnD03z3YyTeKSxYUEFJ4/YK1gE5ssgD3S2NnPoeYezplr3Q+TWVmWQ1ZKgvUDm5hlAeyRTc6pd86em+dxJZErwe9j7fwCXjzYYpO0m5hkAeyRTYdbSU/ys2xWltelRLTzF+RT195HTWuv16UYE3IWwB555VArZ86x8b8nc54zQ9zGAy0eV2JM6NlvvwfaegbZe6yLc6z74aTmF6ZTnJXMiwdtXggTeyyAPbDZ+n+nTERYO7+Alw62EAhYP7CJLRbAHnjlcCvJCT5WlNn8D1Oxdn4+LT2D7Gvs8roUY0LKAtgDmw63sqoih+QEm/93Ks5zzhRt/cAm1lgAu6S8ohIRedvFl5zGa7WtPPHz70/4vIgdlDFeWW4alflpvGT9wCbGuD0dZdw6UlvD3U/tfdvjVc09rH+1no/+zd9R8Y9fm/C9d1y52O3yos7a+QX84dV6hkcCNnLExAz7SQ6zuvY+fAKl2SlelxJV1s7Pp2tgmNfrbHpKEzssgMOsrr2P4qwUEq0VNy2j/cAvHrR+YBM7LAXCaGgkwLHOfmblpHpdStQpyEhmSUmmjQc2McUCOIyOdvQTUCizAJ6RtfML2FLVRv/QiNelGBMSFsBhVNfehwClOdb/OxNr5+czMBxgW02b16UYExIWwGFU195HYWayjf+doXPm5eH3yfEzSRsT7SyAw2Q4EKCho5/Z1v0wY5kpiZw+O5uNB6wf2MQGC+AwaewcYCSgzM61AJ6U+CY9OGX08pdf38PWw834klLf8nh5RaXX1RszbXYgRpjUtfcBMCvbAnhSGpjw4JWxqlt6eHRHPbf/7EXm5Kcff9wOXjHRyFrAYVLX1kd+ehKpSdb/eypm5aTiEzjS1ud1KcacMgvgMAio0tBh439DIdHvoyQrhVo7Q4aJARbAYdDSPcjgSIBZNvwsJMry0mjqGmBg2MYDm+hmARwG9aP9v9YCDony3FSUYLeOMdHMAjgM6tv7yEhOICsl0etSYkJJVgp+n1g/sIl6FsAuU1XqO/qt+yGEEvw+SrNTLIBN1LMAdllX/zDdA8M2/CzEynJTaeoeoM/mhTBRzALYZfUd1v/rhrLcNMD6gU10swB2WX17P0l+H/kZSV6XElNKslJI8AlH2mw4moleFsAuq2/vozQnBZ+d6y2k/D5hVk6q9QObqGYB7KL+oRFaegat/9clZbmptPQM0js47HUpxsyIBbCLGjr6AWwEhEvKnX5gawWbaGUB7KJ65wScxVkWwG4oykwmye+zADZRywLYRfXtfRRl2gk43eLzCbNyUqi1HXEmSlkyuMWfyLHOAet+cFl5bhrtvUP4M/K8LsWYabMAdklyyQJGVG38r8vKnAnuUypWeFyJMdNnAeyS5LKlAJRmWwvYTQWZySQn+EiuON3rUoyZNtcDWET8IrJdRP7g3M8TkadFZL9znet2DV5ILltGbloiaUl20hE3+USYnZNqLWATlcLRAv4ssGfM/TuBZ1R1IfCMcz+mBAJK8uzTrPshTMpyU0nMLbWj4kzUcTWARaQMeBfw4zEPXwfc79y+H7jezRq8cLCpG39qph2AESblecHxwHa6ehNt3G4B/zvwRSAw5rFiVW0AcK6LJnqjiNwmIltEZEtTU5PLZYbW5qo2wA7ACJf89CRGejt46ZAFsIkurgWwiFwLNKrq1pm8X1XvUdU1qrqmsLAwxNW5a0tVKyPdbWSn2gTs4SAi9Ne8zssHW1BVr8sxZsrcbAGfD7xHRKqAXwGXisgvgGMiUgrgXDe6WIMnNle30l+3G7EJeMKmv+Y16jv6qbGTdZoo4loAq+qXVLVMVecANwN/VtVbgceAdc7L1gHr3arBC0c7+qlt7WPgyC6vS4kr/TWvAdYPbKKLF+OA7wKuEJH9wBXO/ZixpboVgIEjuz2uJL4MtxyhMDPZ+oFNVAnLIFVV3QBscG63AJeFY71e2FLVRlqSn8Fjh7wuJe6snZ/PxgPBfmDr/jHRwI6EC7HNVa2sqsgBDZz0tSa0LlxYSHP3AHsaurwuxZgpsQAOoa7+IfY0dLKm0iaG8cKFCwsAeH5/dA1bNPHLAjiEtte0E1BYMycmj66OeMVZKSwuzuT5/c1el2LMlFgAh9CWqlZ8AqsqLIC9cuHCAjZVtdI3aKerN5HPAjiENle1sXRWFhnJNgGPVy5cVMjgcIBNVa1el2LMSU0pgEXkmak8Fs+GRgJsr22z/l+PnT0nj6QEH8/vs35gE/lO2FQTkRQgDShwpo0cHduTBcxyubaosqu+k/6hAGfNsQD2UmqSn7Pn5Fk/sIkKJ2sBfxLYCixxrkcv64EfuFtadNni/MtrO+C8d+HCAvYe6+JYZ7/XpRhzQicMYFX9nqrOBb6gqvNUda5zWamq3w9TjVFhS1UbFXlpdgZkr4gPEUFEuP2GKwCYf/67jj92okt5RaXHxZt4NaW9Rar6/0RkLTBn7HtU9Wcu1RVVVJUt1a1ctCi6Zm2LKRrg7qf2Bm+q8uMXDnP+x77G1cv/86RvvePKxW5XZ8yEphTAIvJzYD6wAxgd36OABTBQ1dJLc/eg7YCLECJCRV4a1S29dliyiWhTHS+1BliqNtnqhKz/N/JU5KXxxtEumroHKMq0biETmaY6DngnUOJmIdFsW00bWSkJLCjM8LoU46hwTlNU02LzA5vINdUWcAGwW0Q2AQOjD6rqe1ypKspsqWpjdWUuPp/9qxsp0pMTKMhIorq1lzU2NNBEqKkG8NfdLCKadfQOsb+xm+vOsGHRkaYyL53ttW0MDgdISrCDPk3kmeooiL+4XUi02lYTPAHnmbYDLuLMKUhja00bNa29LCiy7iETeaZ6KHKXiHQ6l34RGRGRTreLiwZbq9vw+4SV5dlel2LGKc1OJSnBR1VLj9elGDOhqbaAM8feF5HrgbPdKCjabKluZdmsLNKSbAKeSOP3CZV5aRxu7rHhaCYizahjTFUfBS4NbSnRZ2gkwKu1Hay26Scj1tyCdHoHR2jsGjj5i40Js6keiPG+MXd9BMcFx/2Y4D0NnfQNjdj43whWmR8cjna4uccOEzcRZ6r/N797zO1hoAq4LuTVRJktVaM74CyAI1VaUgIlWSkcbu7h3Hn5XpdjzFtMtQ/4o24XEo221rQxOyeV0uxUr0sxJzC3IJ2XDrXQMzBMuk2WbyLIVEdBlInIIyLSKCLHROR3IlLmdnFeKq+oPOksWus3vs6+F5+Y8DkTOeYWpAPYaAgTcabaHPgp8EvgBuf+rc5jV7hRVCQ4UltzfHatiXT2D/HTjVVcfv37WXn7J972vM2wFTkKMpLISE7gcHMPy2bZcEETOaY6CqJQVX+qqsPO5T4grudebGgPTvZdmm07diKdiDC3IJ3qll6GRwJel2PMcVMN4GYRuVVE/M7lVqDFzcIiXUNHH4l+oSAj2etSzBTML0xnOKDUtNrkPCZyTDWAPwbcCBwFGoD3A3G9Y66+o5+SrBSbgCdKlOWmkZTg42CT9QObyDHVAP4msE5VC1W1iGAgf921qiLc4HCA5q4BG/0QRfw+YW5+OoeauwkE4n4Iu4kQUw3gFaraNnpHVVuBVe6UFPmOdvajwKwc6/+NJvML0+kfClDf0ed1KcYAUw9gn3NaegBEJI+pj6CIOQ3OL3CJ7YCLKpX56fh9Yt0QJmJMNUS/C7woIr8leAjyjcC3XasqwjW095OfkURygt/rUsw0JCX4qMhL42BTNxctLLDx2sZzU2oBO2c//ivgGNAEvE9Vf+5mYZFKVWno6LfhZ1FqfmE6Xf3DNHXb5DzGe1PuRlDV3cBuF2uJCi09gwyOBJhlO+Ci0ryCDIRGDjb22Mk6jefsPC3TVN8e7P+1FnB0Sk3yMzs3lf2NXdhJvo3XLICnqaGjn7QkP9mpiV6XYmZoUVEmbb1DNHcPel2KiXMWwNM02v9rO3Ci1/yidATY39jldSkmzrkWwCKSIiKbRORVEdklIt9wHs8TkadFZL9zHTWT6fYMDNPRN2T9v1EuLSmBsrxU9h/rtm4I4yk3W8ADwKWquhI4A7haRM4F7gSeUdWFwDPO/ajQ0OFMwGMHYES9RUWZtPdZN4TxlmsBrEHdzt1E56IEz6Rxv/P4/cD1btUQag0dffh9QmGmTcAT7eYXZiAC+45ZN4Txjqt9wM7MaTuARuBpVX0FKFbVBgDnusjNGkKpvr2f4sxkEnzWdR7tUpP8lOemsb+x++QvNsYlriaJqo6o6hlAGXC2iCyf6ntF5DYR2SIiW5qamlyrcaqGRwI0dvVTmmP9v7FiYXEGHX1DJBXP97oUE6fC0pRT1XZgA3A1cExESgGc68ZJ3nOPqq5R1TWFhd7P/X6sa4CAwiwb/xszFhRm4BNIX3qJ16WYOOXmKIhCEclxbqcClwNvAI8B65yXrQPWu1VDKNkEPLEnJdHPnPx00pZebGfKMJ5wswVcCjwrIq8Bmwn2Af8BuAu4QkT2Ezyn3F0u1hAyDe395KQlkpYUt5PAxaQlpZkkZOSx8WBcn+DFeMS1NFHV15hgzmBVbQEuc2u9bhidgGdOQZrXpZgQm5ufzkh/N49ur+PiRd53dZn4Yrvzp6C9b4i+oRE7ACMGJfh99L7xAk/sPErPwLDX5Zg4YwE8BTYBT2zr2fUsfUMjPLX7qNelmDhjATwFDR39JCf4yEtP8roU44KBI7uZnZPKw9vqvC7FxBkL4CloaLcJeGKb8t5Vs9l4oJnGzn6vizFxxAL4JPqHRmjtHbQDMGLc9atmE1B47NV6r0sxccQC+CRGJ+CxAzBi24KiDFaUZfPIduuGMOFjAXwSDR19+ASKsyyAY917V81mV32nTdBjwsYC+CTq2/spzEwm0W8fVax798pZ+H3C77Ye8boUEycsVU5gJKAc6+ynNMv6f+NBQUYyly4p4nfbjjA4bIcmG/dZAJ9Ac/cAwwG1CdjjyC1nl9PcPcif3zjmdSkmDlgAn8DxM2DYDri4cdHCQkqyUnhwU63XpZg4YAF8Ag3tfWSmJJCZYmdAjhcJfh83rinjuf1N1DlHQBrjFgvgE6h3zoBs4ssNa8oB+PVmawUbd1kAT8KfWUD3wDClNgFP3CnPS+OCBQX8ZkstIwE7a7JxjwXwJJJnLwGs/zde3XxWBfUd/Ty33/vTYZnYZQE8ieTZp5HgEwoy7AzI8eiKpcXkpSfxkO2MMy6yAJ5E8qzTKMlKwe+zCXjiUVKCj79aPZv/2XOMpq4Br8sxMcoCeAJ9gyMkFc+z8b9x7qazKhgOKL+1I+OMSyyAJ/DakXbEn2A74OLcgqIMzp6Txy83VdvOOOMKC+AJbK1pA+wMyAY+vLaS2tY+nn2j0etSTAyyAJ7Atuo2hlpqSU30e12K8dhVy0ooyUrh/peqvC7FxCAL4HFUla3VbQzU7fG6FBMBEv0+PnhOBc/vb+ZAY7fX5ZgYYwE8zqHmHtp6hyyAzXG3nFNBkt/Hz6wVbELMAnicrdXB/t9+C2DjKMhI5toVpfxu6xG6+oe8LsfEEAvgcbZVt5Gdmshwi52axrxp3do59AyO2JA0E1IWwONsrW5jdUUOYMOOzJtWluewqiKHn71UTcCGpJkQsQAeo6N3iP2N3ZxZmet1KSYCfWTtHA4399j8ECZkLIDH2FYb7P9dbQFsJnDN8lIKM5O578Uqr0sxMcICeIxt1W34fcLKshyvSzERKCnBx63nVLJhb5OdOdmEhAXwGFur2zitNJP05ASvSzER6sPnVZKa6Oee5w55XYqJARbAjuGRADtq2zmzwrofzORy05O46axy1u+oo6HDTllkTo0FsOONo130Do5w5pw8r0sxEe7jF8wloPCTFw57XYqJchbAjm3OBDw2AsKcTHleGu86vZRfvlJDR58dmGFmzgLYsbW6jZKsFGbZDGhmCm67aB49gyP84uVqr0sxUcwC2LG1uo0zK3MRsTNgmJNbPjubixYVcu8Lh+kZGPa6HBOlLICBY539HGnrs/G/Zlo+e9lCWnsGrRVsZsy1ABaRchF5VkT2iMguEfms83ieiDwtIvuda89Tb1u19f/GNfEhItO+rJmTR9/hbfzzI5vpHbRWsJk+Nwe8DgOfV9VtIpIJbBWRp4GPAM+o6l0icidwJ/D3LtZxUluq20hO8LG0NMvLMoxXNMDdT+2d0Vvr2/v4zdYjPPByDf/ronkhLszEOtdawKraoKrbnNtdwB5gNnAdcL/zsvuB692qYaq2VrexsiyHpATrkTHTMysnlb7D2/jRcwfpGxzxuhwTZcKSOCIyB1gFvAIUq2oDBEMaKApHDZPpHxphV32H9f+aGevY+CDN3YM2YbuZNtcDWEQygN8Bn1PVzmm87zYR2SIiW5qa3Jt96vW6DoZG1Pp/zYwN1O3hHYsL+cGzB2jvHfS6HBNFXA1gEUkkGL4PqOrDzsPHRKTUeb4UmPB0s6p6j6quUdU1hYWFrtU4egaM4BzAxszM31+zhK6BYX644aDXpZgo4uYoCAHuBfao6t1jnnoMWOfcXgesd6uGqdha3cbcgnTyM5K9LMNEuSUlWfzV6jLu21hFbWuv1+WYKOFmC/h84EPApSKyw7m8E7gLuEJE9gNXOPc9oapsq25jtU3AY0LgjisWIQJ3P73P61JMlHBtGJqqvgBMdljZZW6tdzqqW3pp6Rm0/l8TErNyUvno+XP50XMH+ej5c1hh80qbk4jrcVebq1oBWDPHAtiExl+/Yz4FGcl89dGdjNi548xJxH0A56QlsqAww+tSTIzISknkH955Gq8e6eBXm2u8LsdEuLgO4C1VbaypzMXnswl4TOhcd8Yszp2Xx789sZeW7gGvyzERLG4DuKlrgEPNPZxlE7CbEBMRvnndcnoGhrnrT294XY6JYHEbwFuO9/9aAJvQW1icyScunMdvth7huX12GnszsbgN4M1VbaQk+jh9drbXpZgY9bnLF7KgKIMv/vY1O3OGmVAcB3ArZ5TbBDzGPSmJfu6+cSVN3QN847FdXpdjIlBcpk/3wDC76jus/9e4bkVZDp95xwIe3l7HEzuPel2OiTBxGcDba9oIKBbAJixuv3QBy2dncefDr9lhyuYt4jKANx9uxSewyibgMWGQ6Pfx/VtWMzKi/PUD2+gfsnmDTVB8BnBVG0tnZZGZkuh1KSZOzClI57s3ruT1ug7+6Q+7vS7HRIi4C+DB4QDba9us+8GE3ZXLSvj0JfP55Ss1/HpLrdflmAgQdwG8q76D/qGABbDxxOevWMQFCwr48sOv8+KBZq/LMR6L6QAur6h825lsL7nh4wC8+7ylJzzjrTFuSPD7+MEHVzOvMJ1P/mIr5cvPmdEZmUWE8opKrzfHnCI3z4rsuSO1NW872+3vX62npWeQzz7yygnfe8eVi90szcSx7NREfvKRs3jvD19EL/wk37zrp6QnT/9X0X5Go19Mt4DHU1XqO/qYnZPqdSkmzpXlpnHvujX4UrN4ZHsdfTYyIi7FVQC39gzSPxRgVk6K16UYw4qyHJp+903a+4Z4dHsdA8MWwvEmrgK4vr0fCJ65wJhI0F/zGu88vYTm7gEe21HP0EjA65JMGMVVAB9p7yU92U9Oqo3/NZFjXkEGVy0roaGjnz+81sBwwEI4XsRNAKsqR9r6KMtJs1EOJuIsKs7k8tOKqWnt5U+vH7XTGcWJuAngtt4hegdHKMu17gcTmZbOyuKSRYUcau7hqd1HCaiFcKyL6WFoYx1pC06CYgFsItnK8hyGRgJsPNhCgq+Ry08rsv/YYlgcBXAfGckJZFv/rwk18YU0JNfMyWNoRNlU1UqiX7h4UaGFcIyKiwAe7f+tzLf+X+MCDbztgJ+pmuxginPn5TE0EmB7bTuJfh/nLyg4lQpNhIqLAG7tGaRvyPp/TfQQES5cWMBQIMCW6jYS/T7Onmvzl8SauAjgI219QPDoI2OihYhw6eIihkeUlw61kJbkZ7mdwzCmxE0AZ6YkkJUSF5trYoiIcPlpxfQNjvDnvY1kpiRQmZ/udVkmRGJ+GJqqUtfeR1lOqvX/mqjk9wnvPL2U/PQk/vh6A01dA16XZEIk5gO4uTvY/zvb+n9NFEtK8HHdytkkJ/h57NV6egaGvS7JhEDMB/DoSRAr8qz/10S3jJQE3rNyFv1DI/zx9QbwWZdatIv5AK5p7SUvLcnO/2ZiQmFmMlcsLaaho5+8yz/pdTnmFMV2APsTOdLeZ61fE1MWFWeypjKXzFXX8MtXarwux5yCmA7glLKljASUinwLYBNbzpufT9+hrXz997vYXd/pdTlmhmI7gOeswifYGTBMzPGJ0PyH75KTmsjfPLjNdspFqZgO4NS5qyjNTiUpIaY308SpQF8n37t5FVXNPXx1/U6vyzEzELPJ1Nw9QFLxfOt+MDHtvPn53H7pQh7eVsfvth7xuhwzTTEbwBsPNANQaTvgTIz728sWcs7cPL66ficHGru9LsdMg2sBLCI/EZFGEdk55rE8EXlaRPY717lurf/5/c2M9HVSmJns1iqMiQh+n/C9m1eRkujn9ge328k9o4ibLeD7gKvHPXYn8IyqLgSece6HnKry/P4m+qt24LPDj00cKMlO4Ts3rGBPQyffeXJmU2Oa8HMtgFX1OaB13MPXAfc7t+8Hrndj3QPDAW5cU07Prg1uLN6YiHTpkmI+dG4l//38YV7Y3+x1OWYKwt0HXKyqDQDOddFkLxSR20Rki4hsaWpqmtZKUhL9fP7KxfQd3HRq1RoTyZwzcYy9fPuGNQy11HLzvz+OPzXrbc+PvZRXVHq9BXEvYg8mV9V7gHsA1qxZY2cnNGa8Sc7E0djVz0Oba7nkW4/xrtNLJ50FcLKzcZjwCXcL+JiIlAI4141hXr8xMa8oM4W18ws42NTD7gY7Si6ShTuAHwPWObfXAevDvH5j4sLqihzKclP5y74m2noHvS7HTMLNYWgPAi8Bi0XkiIh8HLgLuEJE9gNXOPeNMSEmIly5tBifCE/uOspIwHrxIpFrfcCqesskT13m1jqNMW/KTEnksiVFPL7zKJsOt3Le/HyvSzLjxOyRcMYYWFicydLSLDZXtVLX3ud1OWYcC2BjYtzFiwrJSk3kyV1H7Si5CGMBbEyMS0rwcdWyYroHhnl27/TG1Bt3WQAbEwdKs1M5Z04ee4928cZRG5oWKSyAjYkTZ83JozQ7hWffaKKzb8jrcgwWwMbEDZ9PuGpZCQB/2nkU/BF7IGzcsAA2Jo5kpyZy+dIijnb2k3fpJ7wuJ+5ZABsTZxYWZXJmRS6Zq6+1s2h4zALYmDi0dn4+/dWv8eVHXmdnXYfX5cQtC2Bj4pDPJzQ99q/kpyfxsfs2U28HaXjCAtiYOBXo7eAnHz2L3sERPnbfZrr6bWREuFkAGxPHlpRk8cMPrmZ/Yzd/88vtDI0EvC4prlgAGxPnLlpUyLeuX85f9jXxuYd2MGwhHDY2ENAYwy1nV9DVP8Q/P/4GyX4f37lhJT6fndDWbRbAxhgAbrtoPgNDAb779D4S/T7++X2n47cQdpUFsDHmuNsvW8jQSID/+PMBOvqG+PebzyAl0e91WTHL+oCNMW9xx5WL+eq1S3li11E+fO8mOmzeCNdYABtj3ubjF8zlP25ZxfbaNt77w43sO9bldUkxyQLYGDOh96ycxS8+fg6dfcNc/4ON/P7Veq9LijkWwMaYSZ0zL58//u0FLC3N4vYHt/Olh1+zAzZCyALYGHNCxVkpPHjbuXzy4nk8tLmWq//9eV7Y3+x1WTHBAtgYc1KJfh9fuuY0fvOptSQn+Lj13lf47K+209Bhc0icChuGZky8Eh8i0x/nKwlJ5Jx/C48OX8cjmw7R+fJv6NyyHh3qn/IyysorqK2pnva6Y40FsDHxSgPc/dTeGb31jisX87d3/B3P72/i4EUfovSyj3BmZS4ryrJJ9J/8H+s7rlw8o/XGGgtgY8yMZKcmcu2KWTR09PHyoVZeONDM1uo2Tp+dzYqybNKTLV5Oxj4hY8wpKc1O5b2rZlPX3sfW6jY2VbWytbqNRSUZrCrPpTAz2esSI5YFsDEmJGbnpDI7J5W23kF21Lazu76TPQ1dFGUms7Q0i8UlmXZY8zgWwMaYkMpNS+Idi4s4b14+bxztYnd9Jxv2NfH8/mbmFqazsCgDSUr1usyIYAFsjHFFSqKfM8pzOKM8h6auAXY3dLL3aBcHGrspv/0BPnH/Zq5cVsLFiwopzkrxulxPWAAbY1xXmJnMxZmFXLiwgIb2fn7yo++zp+AW/mdPIwDzCtM5b14+a+cXsLoyh5KslBkNkYs2FsDGmLDxiTA7N5W2P/+YF/7nHnbVd/LSwRZePNjMo9vreOCVGgDy05NYNjubZbOyWFycSWV+GnPy08lJS4ypYLYANsaEn/jw+caNF/b5SSqeT3LpIrqL59FQPJ+/FFQi/jdjaqS/m5HORoa7WhjpbmWkp42RrpbgdXfr8ccIjEy42kg7AMQC2BgTflM8CGQ4EKCzb5j23kHa+4bo6M3m5ef2UHnGBfQMDNM3OIJO8L60JD8ZyQmkJyeQnhy8nZGcwAPf+BRVzT2U5aaSMIUDRtxmAWyMiVgJPh956UnkpScdf+z3f/sNvnRbMLwDAaVvaITugWF6BofpGRihZ2CYbufS1T/E0Y5++oaCLeLiG/+JS76zgQSfUJabSmV+OnML0plXmM6i4kyWlGSSk5Y0YS2ubF/Y1mSMMSHm84nTyj1xlA0HAvQOjPAvn7mJnz3yJ6pbeqhq7qWqpYctVa30DL7ZZVGclXw8jIPXWSwsznBlDLMFsDEm5iX4fGSl+hio28NNZ1W87Xl/Zj6JBZUkFc6hu6CSmsJKniuoQBKCrWENjDDcVo//wHPUPPvL0NUVsiVNg4hcDXwP8AM/VtW7vKjDGBNnpjEBUSCgdPQN0dwzQHP3IM1dWWx68aGQlhP2ABYRP/AD4ArgCLBZRB5T1d3hrsUYYybj8wm56UnkpiexsCj42LO7N4R2HSFd2tScDRxQ1UOqOgj8CrjOgzqMMcZTXgTwbKB2zP0jzmPGGBNXRHWiUXQurlDkBuAqVf2Ec/9DwNmqevu4190G3ObcXQzMbOZo7xUAsXgCLduu6GLb5a1mVb16/INe7IQ7ApSPuV8GvO1816p6D3BPuIpyi4hsUdU1XtcRarZd0cW2KzJ50QWxGVgoInNFJAm4GXjMgzqMMcZTYW8Bq+qwiPwN8CTBYWg/UdVd4a7DGGO85sk4YFV9HHjci3V7IOq7USZh2xVdbLsiUNh3whljjAnyfjogY4yJUxbAISAiV4vIXhE5ICJ3TvD8JSLSISI7nMs/elHndInIT0SkUUR2TvK8iMh/ONv9moisDneNMzGF7YrW76tcRJ4VkT0isktEPjvBa6LuO5vidkXld4aq2uUULgR3JB4E5gFJwKvA0nGvuQT4g9e1zmDbLgJWAzsnef6dwJ8AAc4FXvG65hBtV7R+X6XAaud2JrBvgp/FqPvOprhdUfmdWQv41MXsodWq+hzQeoKXXAf8TINeBnJEpDQ81c3cFLYrKqlqg6puc253AXt4+1GmUfedTXG7opIF8Kmb6qHV54nIqyLyJxFZFp7SXBfLh5VH9fclInOAVcAr456K6u/sBNsFUfid2XzAp26iMwSOH1qyDahU1W4ReSfwKLDQ7cLCYCrbHo2i+vsSkQzgd8DnVLVz/NMTvCUqvrOTbFdUfmfWAj51Jz20WlU7VbXbuf04kCgiBeEr0TVTOqw82kTz9yUiiQRD6gFVfXiCl0Tld3ay7YrW78wC+NSd9NBqESkR51zaInI2wc+9JeyVht5jwIedPevnAh2q2uB1UacqWr8vp+Z7gT2qevckL4u672wq2xWt35l1QZwineTQahH5lPP8fwHvBz4tIsNAH3CzOrtuI5mIPEhw73KBiBwBvgYkwvHtepzgXvUDQC/wUW8qnZ4pbFdUfl/A+cCHgNdFZIfz2JeBCojq72wq2xWV35kdCWeMMR6xLghjjPGIBbAxxnjEAtgYYzxiAWyMMR6xADbGGI9YAJu4ISIbRCRqzx9mYo8FsDHGeMQC2HhGRNJF5I/OBCo7ReQm5/F/FJHNzmP3jDnCaYOI/F8Rec6ZG/YsEXlYRPaLyLec18wRkTdE5H5nvtvfikjaBOu+UkReEpFtIvIbZ56B8a856fqc190qIpuceWh/JCJ+5/H/FJEtzhy23xjz+ioR+Yaz7tdFZEnoP10TDSyAjZeuBupVdaWqLgeecB7/vqqe5TyWClw75j2DqnoR8F/AeuAzwHLgIyKS77xmMXCPqq4AOoG/HrtSZ46ArwCXq+pqYAtwxyQ1nnB9InIacBNwvqqeAYwAH3Te+w8aPGX6CuBiEVkxZrnNzrr/E/jCVD4sE3ssgI2XXgcuF5F/FZELVbXDefwdIvKKiLwOXAqMnVrwsTHv3eXMFTsAHOLNSWZqVXWjc/sXwAXj1nsusBTY6Bzaug6onKTGk63vMuBMYLOzrMsITs4PcKOIbAO2O9uwdMxyRyeU2QrMmWTdJsbZXBDGM6q6T0TOJDg3wb+IyFPAvwE/BNaoaq2IfB1IGfO2Aec6MOb26P3Rn+fxx9ePvy/A06p6yxTKPNn6BLhfVb/0lhWIzCXYsj1LVdtE5L5JtmME+z2MW9YCNp4RkVlAr6r+AvgOwdMEjYZUs9Mv+/4ZLLpCRM5zbt8CvDDu+ZeB80VkgVNHmogsmsF6AJ4B3i8iRc6y8kSkEsgCeoAOESkGrpnh8k0Ms7+8xkunA/9HRALAEPBpVW0Xkf8m+C9/FcHpPqdrD7BORH4E7CfYz3qcqjaJyEeAB0Uk2Xn4KwTPNTYtqrpbRL4CPCUiPmc7PqOqL4vIdmAXwe6KjSdajolPNhuaiSkSPGXNH5wdeMZENOuCMMYYj1gL2BhjPGItYGOM8YgFsDHGeMQC2BhjPGIBbIwxHrEANsYYj1gAG2OMR/4/IHTNqf4qBdYAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 5\n", "n = 5\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(exp_pop, size = n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde = True)\n", "plt.title('Distribution of Sample Means for n = ' + str(n))\n", "plt.xlabel('sample mean')\n", "plt.ylabel('count')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sampling Distribution for Sample Size n = 15" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 15\n", "n = 15\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(exp_pop, size=n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde=True)\n", "plt.title(\"Distribution of Sample Means for n = \" + str(n))\n", "plt.xlabel(\"sample mean\")\n", "plt.ylabel(\"count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sampling Distribution for Sample Size n = 30" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 30\n", "n = 30\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(exp_pop, size=n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde=True)\n", "plt.title(\"Distribution of Sample Means for n = \" + str(n))\n", "plt.xlabel(\"sample mean\")\n", "plt.ylabel(\"count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sampling Distribution for Sample Size n = 50" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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gKH2371sxm3tvXsfx1h5u+PUmawmbGSeUBbgKqFLVTc71B/EX5BMiUgjgnNeFMIOJEFuONdPY2ce7Ts0jIc4btOWeMTebX68/nWONXdx05+u09fQHbdnGhFrICrCqHgcqRWSRc9PFwF7gUWC9c9t64JFQZTCRobN3gDfKm1iQn8q83NSgL/+s+Tn84oY17Dvexifv2mwb5syMEepREF8AfisiO4GVwL8APwAuFZGDwKXOdRPFNh1tYkiVc+bnBGV5xSWliMjbThedVkDNwz/g9fIm5lz1tXfcLyIUl5QG5fWNCZaQ7oihqtuBtWPcdXEoX9dEjtbufnbXtLJsdgaZyfFBWWZVZcW44403HWnkNS7msquv5fSy7Lfd95XLFo35HGPcYnvCmZDaVtGMwDuKYaicMTebpq4+XjncSHZKPPPzgt/lYUyw2GxoJmS6+wfZU9PGollppCaG57teRLj0tAIK0hN4es8JmrtsZISJXFaATcjsrm5lYEhZXZIV1tf1eT1cuawQjwf+tLOW/sGhsL6+MYGyAmxCQlXZXd1KUVYSuakJYX/99MQ4Ll8yi8bOPp7dV0co5zwxZqqsAJuQqGjqoq1ngKWzM1zLUJqTwrq52ew73s6emjbXchgzHtsIZ0JiT00biT4P8/NSXM2xbm42NS3dvHCgHl/2HFezGDOatYBN0PX2D3KkvpNTC9Pxed39iIkIly2ehc8r5L7va7aThokoVoBN0B2q72BQNbBJ08Uz5k4TJztNVmqij0tOKyBh1gJmXfqpSb2W7bxhQsm6IEzQ7T/RTkZSHAVpAWx806GAJnEfaSo7VMzPS6V965/IWPcBPvGZL1KUlRyy1zImUNYCNkHV2TtAVVM3iwrSIu5oFc3P3UlGUhzP7D1hQ9NMRLACbILqcH0HCiwsiLw90HSgl0tPK6CtZ4CXDzW4HccYK8AmuI7Ud5KZFEdOSnDmfQi2OVlJrCzKZEdVK9XN3W7HMTHOCrAJGolPprK5i3l5KRHX/TDS2Qty/F0Rb55gwLoijIusAJugSZq3hiGFeRE+AU6c18NFp+bT2t3PloqTHpDbmJCyAmyCJnnBOpLivBRmTHyUY7eVZCezMD+VN8qbae22o2gYd1gBNkExOKQkzl1FWU4yngjufhjpvIW5eARePGAHfTXusAJsgmJXdSve5AxKc9zd9Xgy0hLjOKMsmyMNnRxt6HQ7jolBVoBNULywvx7VIUqyA9vBIVKsKskiKzmOvxysZ2jIZkwz4WUF2ATFCwfq6Ks9RFJ88I54HA5ej3D2/Fyau/p587jNmGbCywqwmbbW7n62V7bQXb7V7ShTMj8vhYL0BDYdbWJgyIalmfCxAmym7fWjTQwp9JRvdzvKlIj4W8HtPQPsqmoddefkJwuyCXxMoGwyHjNtm440Eu/z0FszuUl1IklJdjJFWUm8Ud7MktkZxPuctkmYJgsysclawGbaNh1tYmVxJgzO7PG0Z8/Pobt/kB1VLW5HMTHCCrCZlraefvbUtHLmvBy3o0xbYUYSpdnJbK9ssb5gExZWgM20bC739/+eOTfb7ShBsbo0i66+QfYfb3c7iokBVoDNtGw60kScV1gV5kPPh0pxVhK5qfFsrWixIymbkLMCbKbltaNNrCjKnHHjf8cjIqwpyaKps49jjV1uxzFRzgqwmbKO3gF2V0dH/+9ICwvSSE3w2UxpJuSsAJsp23KsmcEhZd286Oj/Heb1CCuLM6lq7iYuf67bcUwUswJspuy1I434PMKa0ujo/x1p6ex0vB4hbcW73Y5iopgVYDNlm440srwog+T46NufJyHOy4L8VFIWX2hHzTAhYwXYTEnvwCC7q9s4vSy6uh9GWlKYjicxlUP1HW5HMVHKCrCZkj01bfQNDrGqJNPtKCFTlJVEf3Mte2psljQTGlaAzZRsr2gBiJrxv2MRETp2PUNVczctXX1uxzFRKKQFWETKRWSXiGwXkc3Obdki8oyIHHTOo/c/OIptq2yhMCORgvTIP/7bdHTu3ogAe2utFWyCLxwt4Hep6kpVXetcvw3YqKoLgY3OdTPDbK9sjuruh2GD7Y2U5CTzZm07Q7ZnnAkyN7ogrgI2OJc3AFe7kMFMQ0NHL5VN3f4Z0GLA4sJ0OnoHqGnpdjuKiTKhLsAKPC0iW0TkFue2AlWtBXDO88d6oojcIiKbRWRzfb0dtTaSxEL/70hzc1PweYSDJ2w0hAmuUBfgc1R1NXAF8DkROT/QJ6rqHaq6VlXX5uXlhS6hmbRtlc14PcLS2RluRwmLOK+HspwUDtV3WDeECaqQFmBVrXHO64DfA2cAJ0SkEMA5rwtlBhN82ytbOK0wLWom4AnEwoJUuvoGrRvCBFXICrCIpIhI2vBl4DJgN/AosN552HrgkVBlMME3OKTsqGyNmf7fYWU5KXg9wsE664YwwRPKFnAB8JKI7ABeB/6kqk8CPwAuFZGDwKXOdTNDHK7voKN3gFXFsdH/Oyze56EsJ5lDddYNYYInZDvxq+oRYMUYtzcCF4fqdU1obXOmaFwZA0PQRluYn8bh+k5qW3qYk5XkdhwTBWxPODMp2ytbyEiKY25OittRwm5u7nA3hB2uyASHFWAzKTurWllelIHHI25HCbvhbojD9Z12uCITFFaATcB6BwY5cKKdpXNiY/jZWObmptDRO0BDh80NYabPCrAJ2P7j7fQPasyM/x1LqdP1Ut7Y6XISEw2sAJuA7a72T0izLIZbwKkJPvLSEqwAm6CwAmwCtqu6lYykOIqzY3sEQFlOMrWtPfT0D7odxcxwVoBNwHZXt7J0TjoisbcBbqSynBRUoaLJDltvpscKsBlTcUkpIvLXkzeOnccaePzeX7799hGnWDErI5FEn8e6Icy0Rd/RFE1QVFVWcPvT+9+6XtfWw31vVHL9Jz/PKd/8uzGf85XLFoUrnqs8IpTkJFPe0IWqxtSXjwkuawGbgNS19wKQn5bgcpLIUJaTQnf/4FvvizFTYQXYBKSuvZd4n4eMpDi3o0SE0pxkAMobrBvCTJ0VYBOQuvYe8tMS7Oe2IzneR35agm2IM9NiBdhMaHBIaejos+6HUYqzkzne1kP/4JDbUcwMZQXYTKips4/BISU/LbqPgDxZRVlJDCk2SbuZMivAZkJ17T0A5KdbC3ik2RlJeASqmq0Am6mxAmwmVN/eS5xXyLQNcG8T7/NQkJ5IZbP1A5upsQJsJlTf0Utuqm2AG0txVjJ1bb30DthuyWbyrACbk1JVGtr7yEu17oexFGUloUC19QObKbACbE6qrWeAvsEh8mwExJgKMxLxesT6gc2UWAE2J1Xv7OmVay3gMfm8HgozEqlqsgJsJs8KsDmp+o5eBMhJjXc7SsQqykqivqOXbpue0kySFWBzUg3tvWQlxxPntY/KeIqz/LslV1s3hJkk+68yJ1Xf0UtumrV+T6YgPRGfR2xDnJk0K8BmXD39g7T3DNgIiAl4PcKs9ETbI85MmhVgM66GDmcDnI2AmNDsTH8/cN+AzQthAmcF2IxreASEtYAnNjszEVU43tbjdhQzg1gBNuOq7+glOd5LSoIdOGUiszL8ExVZN4SZDCvAZlwNHX02/jdACT4vuanx1LRaATaBswJsxubx0dTRZ3vATcLszCSOt/aA2L+VCYx9UsyY4nKKGFS1/t9JmJ2RRP+gEp8/1+0oZoawAmzGNFxEcm0PuIDNzvT3AycULXE5iZkprACbMcXnz8PrEbKSrQAHKi0xjrREHwlFi92OYmYIK8BmTHH588hNjcfjsTmAJ2N2ZhIJRYtRVbejmBnACrB5B1UlPr/MRkBMweyMRHyp2RxrtKNkmImFvACLiFdEtonIH53r2SLyjIgcdM6zQp3BTM7xth68yRm2AW4KCjOSANhW2exyEjMThKMF/CXgzRHXbwM2qupCYKNz3USQvTVtgO2CPBU5qfEM9XWzraLF7ShmBghpARaRIuA9wK9G3HwVsMG5vAG4OpQZzOS9WesUYBsBMWkeEfpqD1gBNgEJdQv4P4GvAyNnKClQ1VoA5zx/rCeKyC0isllENtfX14c4phlpb20b/c01JPi8bkeZkXpr9vNmbRs9NkG7mUBABVhENgZy26j73wvUqeqWqQRT1TtUda2qrs3Ly5vKIswU7a1po6/uqNsxZqzemn0MDCm7q1vdjmIi3ElnWRGRRCAZyHU2lg2PSUoHZk+w7HOA94vIlUAikC4i9wInRKRQVWtFpBCom9YamKDq6B3gWFMX/VaAp6y35gAA2ypaWFuW7XIaE8kmagH/DbAFONU5Hz49AvzsZE9U1b9T1SJVLQOuB55V1RuAR4H1zsPWO8syEWL/8TZUoe/EEbejzFhDXS0UZyfZSAgzoZO2gFX1x8CPReQLqvqTIL3mD4DficjNQAXwoSAt1wTB8AgI64KYnlXFWbxR3uR2DBPhAproVVV/IiJnA2Ujn6Oqdwf4/OeB553LjcDFk8xpwmRvbTsZSXEca7cNn9OxqiSTR3fUUNva/dbYYGNGC6gAi8g9wHxgOzC8aVeBgAqwmTn21raxuDCdnW4HmeFWlfj3L9pe0ULhMivAZmyBHupgLbBYbQf3qDY4pOw/3sZHzih1O8qMd1phGvFeD9sqW7hiWaHbcUyECnQc8G5gViiDGPcdbeigp3+IxbPT3Y4y4yX4vCyZk862CtsQZ8YXaAs4F9grIq8DvcM3qur7Q5LKuGKPswFucaEV4GBYVZzFbzcdo39wiDivzXtl3inQAvztUIYwkWFvbRvxXg8L8lPdjhIVVpVkcufLR9lX286yogy345gIFOgoiBdCHcS4b29NGwsLUon3WWstGFaVZAL+mdGsAJuxBLorcruItDmnHhEZFJG2UIcz4aOq7K1ps+6HIJqTmUReWoJNzGPGFWgLOG3kdRG5GjgjFIGMO+rbe2ns7LMNcEEkIqwqzmR7ZYvbUUyEmtJvTVX9A3BRcKMYN+2ptQ1wobCqJIujDZ00d/a5HcVEoEB3xLhmxFUP/nHBNiY4igzvgnyatYCDargfeHtlC+86dcyZV00MC3QUxPtGXB4AyvFPrG6ixN6aNoqzk0hPjHM7SlRZXpSBR2BbRbMVYPMOgfYBfzzUQYy79ta2saTQttQHW3K8j1NnpbPN+oHNGAIdBVEkIr8XkToROSEiDzmHGzJRoKN3gPLGTtsAFyKrSjLZXtHC0JD12pm3C3Qj3G/wz+M7G5gDPObcZqLA8BzAtgEuNFaVZNHeO8Dh+g63o5gIE2gBzlPV36jqgHO6C7DjBEWJ4Q1w1gIOjbd2yLDxwGaUQAtwg4jcICJe53QD0BjKYCZ89ta2kZkcR2FGottRotLcnBQykuLsCBnmHQItwJ8ArgWOA7XABwHbMBclhveAE5GJH2wmzeMRVhZnsvVYi9tRTIQJtAD/M7BeVfNUNR9/Qf52yFKZsBkYHGLf8XaWWPdDSK0uyeJAXTttPf1uRzERJNACvFxV3/r9pKpNwKrQRDLhdKShk94BmwM41NaUZqHqP0KGMcMCLcAe57D0AIhINoHvxGEi2Fsb4GwMcEitKM5ABLbaBO1mhECL6I+AV0TkQfy7IF8LfC9kqUzY7K1tI97nYV5eittRolpaYhyLCtLYcswKsPmrgFrAztGPPwCcAOqBa1T1nlAGM+Gxt6aNRQVpdsSGMFhdmmU7ZJi3Cfi/TlX3qupPVfUnqro3lKFMeKjqW0dBNqG3xtkh42Cd7ZBh/KzZE8NOtPXSZHMAh82aUv9mFOsHNsOsAMewXdWtADYELUxKc5LJTom3fmDzFivAMWxXdSsegSWzbQREOIgIq0uy2GoF2DisAMewXVUtLMhPJSne63aUmLG6NJMjDZ002REyDFaAY5aqsqu6jWVzMt2OElPWlPj7gbdZP7DBCnDMOt7WQ0NHL8vmWP9vOC0vysTnEdsQZwArwDFrV5V/A9yyokx3g0Qj8SAiY56SE3x0Vu/nR3f9/m23F5eUup3auMB2J45Ru50NcDYGOAR0iNuf3j/u3S/sr2d3TStfe3IfHo9/BrqvXLYoXOlMBLEWcIzaWd3KKQVptgHOBYWZiQwMKQ0dvW5HMS6zAhyDVJXd1a0snWPDz9wwy5n4vra1x+Ukxm1WgGNQbWsPDR19LC+yAuyGtAQfqQk+K8AmdAVYRBJF5HUR2SEie0Tkn5zbs0XkGRE56JxnTbQsE1zDe8BZC9gdIsKsjERqWrvdjmJcFsoWcC9wkaquAFYCl4vImcBtwEZVXQhsdK6bMNpV1YrXI7YBzkVzMpNo7xmwI2TEuJAVYPUbnvYpzjkpcBWwwbl9A3B1qDKYse2qbmVhfiqJcbYBzi1zMpMAqG62VnAsC2kfsHME5e1AHfCMqm4CClS1FsA5zx/nubeIyGYR2VxfXx/KmDHFvwdcK8us+8FVuanxJPo8VFkBjmkhLcCqOqiqK4Ei4AwRWTqJ596hqmtVdW1eXl7IMsaayqZumjr7WF6c6XaUmCYizMlKoqq5y+0oxkVhGQWhqi3A88DlwAkRKQRwzuvCkcH4bav07wK7uiTT3SCGoqxk2noGaOu2fuBYFcpREHkikulcTgIuAfYBjwLrnYetBx4JVQbzTtsqWkiO97KoIM3tKDGvKMvfD1zVYt0QsSqUuyIXAhtExIu/0P9OVf8oIq8CvxORm4EK4EMhzGBG2VbRzPKiDHx2DDjX5aTEkxjnsW6IGBayAqyqO4FVY9zeCFwcqtc14+vpH2RPTRufOn+e21EMTj9wZpJtiIth1gyKIXtqWhkYUlbZBriIUZSVTHvPAN70MQcDmShnBTiGbD3WAsBK2wAXMYb7gRNLlrmcxLjBCnAM2VbZTFFWEvlpiW5HMY6clHiS4rwklix3O4pxgRXgGLKtooXVJTb1RiQREYqykkgsW4mquh3HhJkV4BhR29pNbWsPq6z7IeKU5CTjS8th/4l2t6OYMLMCHCO2V7QAsMpawBGnNDsZ8B8pw8QWK8AxYltlC/E+j82AFoHSEuPoqz/GiwetAMcaOyZcDCguKaX//M+DCAlxV7odx4yh++gW3pg1l66+AZLj7d8yVthfOgZU156grHgxq0qyOPem8Q8WOZIdJDK8eo5soe+Ma3jpYAOXLZnldhwTJtYFEQMSZi9iSP86B62JPD2Vu0lL9PHnN0+4HcWEkRXgGJBQshQBZmfa+N+INTTIhYvyeXZfHUNDNhwtVlgBjgGJxcvIS0sgwWdHwIhkl5yWT0NHH9urWtyOYsLECnCU6+kfJGH2IuZkWfdDpLtwUT4+j/D0HuuGiBVWgKPczqpWxBdv/b8zQEZSHOcsyOXxXbW2V1yMsAIc5TYdaUR1yArwDPGe5YVUNHWxq7rV7SgmDKwAR7lNR5vorz9mR0CeId69eBZxXuFPO2vdjmLCwApwFOsfHGLLsWZ6Kna5HcUEKCM5jnMX5PLHnbUTjoYoLilFRCZ9Ki4pDdPamInYjhhRbGdVK939g/RW7nY7ipmEq1fN4Uv3b+e1o42cPT933MdVVVZw+9OB7Vgzku1kEzmsBRzFNh1tBPyD/M3McdniWaQl+HhwS5XbUUyIWQGOYi8dbODUWWkMdbe5HcVMQlK8l/eumM0Tu47T0TvgdhwTQlaAo1Rn7wBvlDdxwSl5bkcxU/DBNUV09w/yyPZqt6OYELICHKVePdxI/6BaAZ6hVpdksrgwnXtePWZjgqOYFeAo9eLBepLivKwpswnYZyIRYf3Zpew73s6mo01uxzEhYgU4Sr1woJ6z5+fY/A8z2PtXzCEjKY7fvHzU7SgmRKwAR6Hyhk6ONXZxwSLrfpjJkuK93HRWKU/tOcEBO15cVLICHIVeOOA/tI31/858Hz9nLsnxXn7+3CG3o5gQsAIchV44UE9pTjKlOSluRzHTlJ0Sz0fXlfDojhoO1XW4HccEmRXgKNM7MMirhxut9RtF/uaC+STH+/i3J/e5HcUEmRXgKPPG0Wa6+wetAEeR3NQEPn3BPJ7ee4LXbUREVLECHGWe2nOcxDgPZ83PcTuKCaKbz51HYUYi//DIbgYGh9yOY4LECnAUGRpSntpznAtPybdDm0eZpHgv//i+Jew73s5vXi53O44JEivAUWRrRTN17b1cscwOax6N3r2kgItPzedHz+znUJ0NS4sGVoCjyJO7jxPv9XDRqfluRzEhICJ8/5plJMf7+OJ928Frv3JmOivAUUJVeWL3cc5dmEtaYpzbcUyI5Kcn8q8fWM7e2jYyz7vR7ThmmkJWgEWkWESeE5E3RWSPiHzJuT1bRJ4RkYPOuU1WEAS7q9uobunm8iXW/RDtLl1cwEfXlZCx7gNUNHW5HcdMQyhbwAPArap6GnAm8DkRWQzcBmxU1YXARue6maYndtfi9QiXLi5wO4oJg2+9ZzF9DRU8tcfmDJ7JQlaAVbVWVbc6l9uBN4E5wFXABudhG4CrQ5UhVqgqT+4+zpnzsslKiXc7jgmDpHgvDX/4Pv2DQzyxq5bBCY4fZyJTWPqARaQMWAVsAgpUtRb8RRqwLUbTtLe2jSMNnVy+tNDtKCaM+hsrufjUAmpae3jlcIPbccwUhLwAi0gq8BDwZVUN+Ng4InKLiGwWkc319fWhCxgFHtpSTZxXeO8yK8CxZtGsNFYUZbC1ooWDNjRtxglpARaROPzF97eq+rBz8wkRKXTuLwTqxnquqt6hqmtVdW1enu1WO57+wSEe2V7NJacVWPdDjDpvYR6z0hP58946mrv63I5jJiGUoyAE+DXwpqrePuKuR4H1zuX1wCOhyhALXthfT2NnHx9YXeR2FOMSr0e4YtksPB54fFctA0O2q/JMEcoW8DnAjcBFIrLdOV0J/AC4VEQOApc6180UPbilipyUeJt8PcalJ8Zx6eICGjr62HTEJuyZKUK2K42qvgTIOHdfHKrXjSXNnX1s3HeCm84qI85r+9TEunm5qSyZnc6WY83MzU1hdmaS25HMBOy/dgZ7dEcN/YNq3Q/mLectzCUt0cfTe0/QN2BdEZHOCvAM9uCWKhYXprN4drrbUUyESPB5uXRxAa3d/bx6uNHtOGYCVoBnqO2VLeyqbuW604vdjmIiTFFWMsvmZLCjuoXGjl6345iTsAI8Q939ajkp8V6uWT3H7SgmAp01P4d4r4cXDtajanvJRSorwDNQY0cvf9xRywfWFNnMZ2ZMSXFezpyXQ2VTN0caOt2OY8ZhBXgGemBzJX2DQ9x0VqnbUUwEWz4ng5yUeP5ysMHGBkcoK8AzzMDgEL99rYJzFuSwID/N7Tgmgnk8wvmn5NHa3c/Oqla345gxWAGeYTbuq6O6pZsbzyxzO4qZAUqykynOSmLLsWY7mGcEsgI8w9zyw/sYaKvjiuVzEJGATmYGEE/Af8/J/l3Xzc2hq2+QXdXWCo40dlCpGWR7ZQtScArvWpjL6qfeDPh5X7lsUQhTmaDQIW5/ev+knhLo33VOVhJFmf5W8LI5GVNJZ0LEWsAzyC9fOMxgTwdLZ9s/kZmcdfOy6ewbZE9NwDPCmjCwAjxDHG3o5Mk9x+nY+ififfZnM5MzJzOJ2ZmJbD7WbEdTjiD2nzxD/M9fjhDn9dC29TG3o5gZSEQ4oyybjt4BUhZf6HYc47ACPAPUtffw4JYqPrC6iKHOFrfjmBmqJDuZ3NR40tdeZXvHRQgrwDPAb14up39wiE+dN9ftKGYGExFWFmcSnz+XV2yinohgBTjCNXf2cfcr5bx3+Wzm5aW6HcfMcIsK0hjsbObXLx11O4rBCnDEu/Plo3T2DfL5dy1wO4qJAj6vh/Ztj/PsvjoO13e4HSfmWQGOYK3d/dz1cjlXLJ3Folm227EJjvZtTxDv9fCbl60V7DYrwBHsrpfLae8d4PMXWevXBM9QVwtXrZzNQ1uqae3udztOTLMCHKHae/r59UtHuHRxAUtsxwsTZOvPLqO7f5AHt1S5HSWmWQF2SXFJ6Un38y9610dp6xng7q9fb/M6mKBbOieDtaVZ3PNqOUNDNiTNLbZLjEuqKivG3fe/b2CI37xylFnpiXzpnsffdp/N62CC5cazSvnS/dt58WA9Fy7KdztOTLIWcATaVd1KT/8Q6+bmuB3FRLErlhaSm5rAPa8ecztKzLICHGH6B4fYcqyZkuxkZmUkuh3HRLF4n4ePrCvh2f11VDR2uR0nJlkBjjC7qlvp7h9k3dxst6OYGPDRdSV4Rbh3k7WC3WAFOIIMOK3foqwkZmcmuR3HxICC9ETevWQWD7xRSXffoNtxYo4V4Aiyp6aNrr5Bziiz1q8Jn5vOKqW1u5/HdtS4HSXmWAGOEINDyuZjzRRmJFKUZa1fEz5nzM3m1Flp3PVKuc2SFmZWgCPEm7VtdPQOsG5uto33NWElItx4Vil7a9vYWtHsdpyYYgU4Agw5rd/8tARKspPdjmNi0NUr55CW6ONuG5IWVlaAI8CBE+20dvdzhrV+jUtSEnx8aE0xj++qpa69x+04McMKsMuGVHm9vInc1Hjm5aa4HcfEsBvPKqV/ULn/9Uq3o8QMK8AuO1zXQXNXP6eXWevXuGtubgrnn5LH/26qoH9wyO04McEKsIvUaf1mJcexIN+OdmHct/6sUo639fDM3hNuR4kJISvAInKniNSJyO4Rt2WLyDMictA5zwrV688ERxs6aejo4/SybDzW+jUR4MJF+RRlJbHhlXK3o8SEULaA7wIuH3XbbcBGVV0IbHSux6zXy5tIT/SxqMCOdmEig9cj3HhmKZuONrH/eLvbcaJeyAqwqr4INI26+Spgg3N5A3B1qF4/0iWWreJEW6+/9eux1q+JHNeuLSbB5+HuV8vdjhL1wt0HXKCqtQDOecxOQppx9nWkJvg4tdBavyayZKXEc9XK2Ty81Q5ZFGoRuxFORG4Rkc0isrm+vt7tOEH12pFGEouXsqY0C58nYv8EJobddJb/kEUP2SGLQirc//0nRKQQwDmvG++BqnqHqq5V1bV5eXlhCxgOP332EIMdzSydne52FGPGtHROBqtLMrn3tWN2yKIQCncBfhRY71xeDzwS5td33daKZl461EDbGw/j81rr10Su9WeXcaShk5cONbgdJWqFchjafcCrwCIRqRKRm4EfAJeKyEHgUud6TPnZs4fITI6jfdsTbkcx5qT8hyyK5zcvH3U7StQK2UE5VfXD49x1caheM9Ltrm5l4746br30FL7Yb/vbm8gW7/PwsbPL+OHTB9hT08qS2RluR4o69hs4jH723CHSEn2sP6fM7SjGBOTGs8pITfDx388fdjtKVLICHCYHTrTzxO7jfOzsMtIT49yOY0xAMpLiuPGsUv60q5Yj9R1ux4k6VoDD5GfPHSI53svHz5nrdhRjJuUT58wl3uvhly8ccTtK1LECHAZH6jt4bEcNN55ZSnZKvNtxjJmUvLQErj+9mIe3VVHT0u12nKhiBTgMfvrsIeJ9Hj51/jy3oxgzJbdcMB9V+Pnzh9yOElWsAIfY0YZO/rC9mhvWlZKbmuB2HGOmZE5mEtefUcz9r1dyrLHT7ThRwwpwiP3suUPEeT3ccoG1fs3M9sWLFuLzCv/xzAG3o0QNK8AhdKyxk99vq+Yj60rIT0t0O44x05KfnsjHzp7LIztq2He8ze04UcEKcBAUl5QiIu84rbnxGwz09fLPHzn/HfcZM5MMf8a/+f/WMtjdwfmf++GYn/mRp+KSUrdjR7yQ7QkXS6oqK7j96f1vu621u5+7Xy1n2ZwMvvzwq+94zlcuWxSueMZM28jP+OvlTbyamMqtD2xnTlbSuM+xz/jErAUcIpvLmxCENaUxfdQlE4VWFWeSmuDjhQP1DKnNlDYdVoBDoKWrj721bSyZnU6a7fVmokyc18N5C3Op7+hlT7X1BU+HFeAQePVIIx4RTp+b7XYUY95JPBP23060zWJhfipzMpN45UgDPf2DLqxEdLA+4CCrb+/lwIkO1pZmkZpgb6+JQDr0jm0WExndnysiXHBKHve9XsGrRxp516KYPbrYtFgLOMhePtxAgs/DWuv7NVEuLy2B5UUZ7Kpq5XibTa86FVaAg6iquYtjjV2cXpZNQpzX7TjGhNxZ83NISfDx570nGBgacjvOjGMFOEhUlb8cbCA1wceKIpu42sSGBJ+Xi07Np7GzjzfKm92OM+NYAQ6SPTVt1LX3cs6CHDvWm4kpc3NTOHVWGpvLm6hv73U7zoxilSIIPAkpvHK4kdkZiSwqSHM7jjFhd8EpeSTGeXl673HripgEK8BBkHHeDfT0D3LhonzbzdjEpMQ4Lxeflk9DRx8vH2x0O86MYeOkpmlvTRtpq65keVEGeWk23aSJXfNyU1lZnMn2yhaKssffRdn8lbWAp6FvYIivPbiDoe52zpyX43YcY1x3zoIc8tMSeGbvCbxpuW7HiXhWgKfhJ88eZE9NG41P/oREG3ZmDD6PhyuWzkIV8q7+hu0lNwErwFO0taKZnz13iA+uKaL70Ca34xgTMTKT47lsSQHxhQv42oM7UZuwZ1xWgKegq2+AW3+3g8KMJP7xfYvdjmNMxJmfl0rLCxt4bEcNP3nWjiM3HivAk6Sq3PbQLsobO/nhh1bYbGfGjKNt00Ncs3oOtz9zgN9vq3I7TkSyURCTdMeLR3h0Rw1fe/cizppvG96MOZnvX7OM2pYevvp/O0nweblyWaHbkSKKtYAn4dEdNXz/iX28Z3khn71wvttxjIl4CT4vv1q/llXFmXzxvm38ee8JtyNFFCvAAXpqz3Fu/d12zpibzY8+tMJ2uDAmQCkJPu78+OksmZ3OZ3+7lcd21LgdKWJYAQ7AH7ZV87nfbmXJ7Ax+tX6tDTkzZpLSE+O4+xPrWFGcwRfu28bPnz9koyOwAnxSA4ND/PtT+/jyA9tZW5bFPTefQbptdDNmSjKS47jn5nW8f8Vs/u3J/fztQzvp7ovtccK2EW4ch+ra+duHdrHlWDPXrS3mn69eSrzPvq+MmY7EOC//ed1KSnOS+cmzh9hyrJn/uG4ly4sy3Y7mCivAo9S0dPOLFw7zv5sqSI738uPrV3LVyjluxzImang8wq2XLeLMeTnc+rsdXPPzV/j0BfP59IXzY+4wXlG9tsUlpVRVVkz4OG96PkllK0haeBZJ89YQ5/PxobXF3HrZKeSm2gQ7xkyJc/DPk/EkpJB1yd/w0yHlx3/cjLz5NAefvJMEX+i3swRaH0YqKi6hsuJY0DJEbQFu7+mntqWTbz68k77BIfoG/Kde53J79wAt3X00dfbR1jMAQEqCl5rn72fXH35OUVayy2tgzAw3iYN/Hm/r4eVDSVSlXMuZ/7KRD6wu4vozSliQnxqyeFWVFdM+OOl0uVKAReRy4MeAF/iVqv4g2K+x9rt/puizG7h309jfcHFeITMpnoL0RFaVJFGclUR2Sjy3fmcDRVl3BTuOMeYkZqUncs2qOXzzU9dy5b/cyV2vlPOrl44yLy+F8xfmcc6CXJbMTqcwIzEoQ0CHhhRPYipNnX109Q3Q1TdId98gXX2DdPUN0N3vvzwwpAyOOKWd/v+CsLZ/FfYCLCJe4GfApUAV8IaIPKqqe4P5Ot96z2l89jOf5oavfo94r4d4319PCc51G8trTOQQEXoqdvLzj66hvr2Xx3bU8MKBeu5/o4K7XikHID3Rx/z8VGalJ1KQnkh6UhwJPg+JcV4SfB48IvQNDNI3OERv/xDd/YM0d/XT3NlHc1cfLV39NHX10dzZR/GX7uee197enSD4NxQmx3tJiveSGOfFK4LX4z8daa4O6jq70QI+AzikqkcAROR+4CogqAX4xrPKuGnHU5xS8F/BXKwxJgzy0hL4xLlz+cS5c+npH2RXdSv7jrezr7aNow2dHKzr4KWDDbT3Dpx0OV6PkJUcR1ZyPFnJ8ZTmJLOyOJOc1Hi++/d/y0e++A8kxfsLbrJTcD0naZg9cej1oK6nhHswtIh8ELhcVT/pXL8RWKeqnx/1uFuAW5yri4DJddacXC7QEMTlRSpbz+gRC+sI0bueDap6+egb3WgBj/X18o5vAVW9A7gjJAFENqvq2lAsO5LYekaPWFhHiJ31HObGngVVQPGI60WA7RxujIk5bhTgN4CFIjJXROKB64FHXchhjDGuCnsXhKoOiMjngafwD0O7U1X3hDlGSLo2IpCtZ/SIhXWE2FlPwIWNcMYYY/xsdhljjHGJFWBjjHFJ1BZgEblcRPaLyCERuW2cx1woIttFZI+IvBDujMEw0XqKSIaIPCYiO5z1/LgbOadLRO4UkToR2T3O/SIi/+W8DztFZHW4MwZDAOv5UWf9dorIKyKyItwZp2uidRzxuNNFZNDZdyA6qWrUnfBv3DsMzAPigR3A4lGPycS/912Jcz3f7dwhWs9vAP/qXM4DmoB4t7NPYV3PB1YDu8e5/0rgCfzjzM8ENrmdOUTreTaQ5Vy+Yiau50Tr6DzGCzwLPA580O3MoTpFawv4rd2dVbUPGN7deaSPAA+ragWAqtaFOWMwBLKeCqSJf+KLVPwF+OT7b0YgVX0Rf/bxXAXcrX6vAZkiMuMOwTvReqrqK6ra7Fx9Df84+hklgL8lwBeAh4CZ+H8ZsGgtwHOAyhHXq5zbRjoFyBKR50Vki4jcFLZ0wRPIev4UOA3/zi67gC+p6lB44oVVIO9FtLkZf6s/qojIHOD/Ab9wO0uoRet8wIHs7uwD1gAXA0nAqyLymqoeCHW4IApkPd8NbAcuAuYDz4jIX1S1LcTZwi2gXdyjhYi8C38BPtftLCHwn8DfqupgtM9YGK0FOJDdnavwT5DRCXSKyIvACmAmFeBA1vPjwA/U37F2SESOAqcCwZ3WyX0xs4u7iCwHfgVcoaqNbucJgbXA/U7xzQWuFJEBVf2Dq6lCIFq7IALZ3fkR4DwR8YlIMrAOeDPMOacrkPWswN/KR0QK8M8sdySsKcPjUeAmZzTEmUCrqta6HSrYRKQEeBi4cYb9WguYqs5V1TJVLQMeBD4bjcUXorQFrOPs7iwin3bu/4WqvikiTwI7gSH8R+Y46bCYSBPIegL/DNwlIrvw/0z/W1WdcdP9ich9wIVArohUAf8IxMFb6/k4/pEQh4Au/C3/GSeA9fwHIAf4udNCHNAZNntYAOsYM2xXZGOMcUm0dkEYY0zEswJsjDEusQJsjDEusQJsjDEusQJsjDEusQJsYoaz2/mMGrJlopsVYGOMcYkVYOMaEUkRkT85cxXvFpHrnNv/QUTecG67w5nJbbgF+x8i8qKIvOnMF/uwiBwUke86jykTkX0issGZM/dBZ0/H0a99mYi8KiJbReT/RCR1jMdM+HrO424QkdeduaV/KSJe5/b/FpHNzjzM/zTi8eUi8k/Oa+8SkVOD/+6amcAKsHHT5UCNqq5Q1aXAk87tP1XV053bkoD3jnhOn6qej3+mrEeAzwFLgY+JSI7zmEXAHaq6HGgDPjvyRUUkF/gWcImqrgY2A18ZJ+NJX09ETgOuA85R1ZXAIPBR57nfdPZSWw5c4MzhMKzBee3/Br4ayJtloo8VYOOmXcAlIvKvInKeqrY6t79LRDY5u09fBCwZ8ZxHRzx3j6rWqmov/vkthifjqVTVl53L9/LOGcPOBBYDL4vIdmA9UDpOxole72L8s+q94SzrYvwT5ANcKyJbgW3OOiwesdyHnfMtQNk4r22iXFTOBWFmBlU9ICJr8M/h8H0ReRr4N+DnwFpVrRSRbwOJI57W65wPjbg8fH348zx6//rR1wV4RlU/HEDMiV5PgA2q+ndvewGRufhbtqerarOI3DXOegxi/4cxy1rAxjUiMhvoUtV7gR/iP0zNcJFqcPplp3I8sBIROcu5/GHgpVH3vwacIyILnBzJInLKFF4HYCPwQRHJd5aVLSKlQDrQCbQ6s9BdMcXlmyhm37zGTcuAfxeRIaAf+IyqtojI/+D/yV+Of8rNyXoTWC8ivwQO4u9nfYuq1ovIx4D7RCTBuflbTGEuaFXdKyLfAp4WEY+zHp9T1ddEZBuwB393xcsnW46JTTYbmokqIlIG/NHZgGdMRLMuCGOMcYm1gI0xxiXWAjbGGJdYATbGGJdYATbGGJdYATbGGJdYATbGGJf8/8JH4S6xHtKdAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the seed for reproducibility\n", "np.random.seed(1)\n", "# set the sample size to 50\n", "n = 50\n", "# list to store sample means\n", "sample_means = []\n", "# iterate the loop to draw multiple samples\n", "for j in range(500):\n", " # draw a sample of size n\n", " sample = np.random.choice(exp_pop, size=n)\n", " # calculate the sample mean\n", " sample_mean = np.mean(sample)\n", " # append the sample mean to the sample_means list\n", " sample_means.append(sample_mean)\n", "# plot the histogram of sample means\n", "sns.displot(sample_means, kde=True)\n", "plt.title(\"Distribution of Sample Means for n = \" + str(n))\n", "plt.xlabel(\"sample mean\")\n", "plt.ylabel(\"count\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Key Takeaway\n", "\n", "* We have tried different distributions to simulate the fundamental idea of CLT. We can see that no matter what the shape of the population distribution is, the plot of samples means approximately tends to normal distribution as sample size increases." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# **Point Estimation**" ] }, { "cell_type": "markdown", "metadata": { "id": "BBYCZHjAG8uU" }, "source": [ "#### Let's see how population mean is estimated by the sample mean\n", "\n", "A non-profit organization sampled the files of the local forest department to come up with the following amounts (in thousands of dollars) of damages for 10 wildfire incidents:\n", "\n", "120, 55, 60, 10, 8, 150, 44, 58, 62, 123\n", "\n", "What is the estimate of the average amount of damage in wildfires, in that area?" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "l_EWV2kfM3BN", "outputId": "ecc82e4e-b2a0-44e6-fa64-c31580d8b437" }, "outputs": [ { "data": { "text/plain": [ "69.0" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# get the sample data\n", "sample = np.array([120, 55, 60, 10, 8, 150, 44, 58, 62, 123])\n", "\n", "# find the mean of the sample\n", "x_bar = np.mean(sample)\n", "x_bar" ] }, { "cell_type": "markdown", "metadata": { "id": "IoxDKLYnNhi_" }, "source": [ "#### Insight\n", "* The estimate of the average amount of damages in wildfires in that area is $69000." ] }, { "cell_type": "markdown", "metadata": { "id": "_6dYoBAwjuyU" }, "source": [ "Usually, point estimate of an unknown population parameter is the corresponding sample statistic. \n", "\n", "For example:\n", "\n", "a. Population mean μ is estimated by the sample mean x̅.\n", "\n", "b. Population median is estimated by the sample median x̃.\n", "\n", "c. Population proportion of success π is estimated by the sample proportion of success p." ] }, { "cell_type": "markdown", "metadata": { "id": "wspseWak5upg" }, "source": [ "# **Confidence Interval**" ] }, { "cell_type": "markdown", "metadata": { "id": "Q-m7is9X8Zkg" }, "source": [ "#### **Let's see how confidence interval is constructed for the population mean when std dev is known**\n", "\n", "It is rarely the case when you know the population standard deviation and not the mean. However, it may not be as unlikely an assumption as it seems. For a tight manufacturing process which is in place for a long time, the variability in the process may be controlled, but with small changes in temperature or humidity, the mean may change.\n", "\n", "\n", "Let's construct the confidence interval for an example where the population mean is unknown and the standard deviation is known.\n", "\n", "\n", "\n", "The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new coffee machine. The mean of the sample is found to be 110 mg. It is known that the standard deviation from all the machines of that manufacturer is 7 mg. Construct a 95% confidence interval for μ, the mean caffeine content for cups dispensed by the machine.\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "eMAb8UKT9J5T", "outputId": "ccf9f89a-1585-46bd-f81e-1ce2b1121ea0" }, "outputs": [ { "data": { "text/plain": [ "array([108.06, 111.94])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# import the required function\n", "from scipy.stats import norm\n", "\n", "# set the values of sample mean and sigma\n", "x_bar, sigma = 110, 7\n", "\n", "# set the value of sample size\n", "n = 50\n", "\n", "# construct the confidence interval\n", "np.round(norm.interval(0.95, loc=x_bar, scale=sigma / np.sqrt(n)), 2)" ] }, { "cell_type": "markdown", "metadata": { "id": "Wg8lB_hy--tZ" }, "source": [ "#### Insight\n", "* 95% of the time, the mean caffeine content for cups of coffee dispensed by the machine will be between 108.06 mg and 111.94 mg." ] }, { "cell_type": "markdown", "metadata": { "id": "Vp65z-lXGYTs" }, "source": [ "#### **Let's see how confidence interval is constructed for the population mean when std dev is unknown**\n", "\n", "The example discussed above is based on the assumption that the population standard deviation is known. However, in the majority of cases, that assumption will not be satisfied.\n", "\n", "When we do not know the population standard deviation, it can be estimated from the sample. In this case, the sample mean follows Student's t distribution with (n-1) degrees of freedom. \n", "\n", "Just like the normal distribution, t-distribution is also very useful in statistical inference. It is a symmetric distribution around 0. For a very large d.f., the t distribution is almost identical to the standard normal distribution.The parameter of t-distribution is known as degrees of freedom.\n", "\n", "Below is the graph of t-distribution for various degrees of freedom(k). We can notice that the distribution approximates to normal as the value of k increases." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 729 }, "id": "HjZtvt2YMK0Y", "outputId": "7c593841-767a-4750-8619-834a33b5554f" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# import the required function\n", "from scipy.stats import t\n", "from scipy.stats import norm\n", "\n", "# set the values for x\n", "x = np.linspace(-3, 3, 100)\n", "\n", "# plot the t distribution for different values of k\n", "fig, axes = plt.subplots(2, 3, sharex=False, sharey=False, figsize=(15, 10))\n", "axes = axes.ravel()\n", "for i, k in zip(range(6), [1, 2, 3, 5, 10, 30]):\n", " ax = axes[i]\n", " ax.plot(x, t.pdf(x, df=k), color=\"blue\", label=\"t dist\")\n", " ax.plot(x, norm.pdf(x), color=\"red\", label=\"normal dist\")\n", " ax.set_title(\"t-distribution for k={0}\".format(k))\n", " ax.legend(loc=\"upper right\", fontsize=10)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "id": "qZwvXTdwR4Ne" }, "source": [ "Let's use the t-distribution to construct the confidence interval for the mean when population standard deviation is unknown.\n", "\n", "The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean of the sample is found to be 110 mg and the sample standard deviation is estimated to be 7 mg. Construct a 95% confidence interval for μ, the mean caffeine content for cups dispensed by the machine." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "aOQK53ojSGfE", "outputId": "b7352d32-e4cf-46d0-9963-6a24766cf5f7" }, "outputs": [ { "data": { "text/plain": [ "array([108.01, 111.99])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# import the required function\n", "from scipy.stats import t\n", "\n", "# set the values of sample mean and sample standard deviation\n", "x_bar, s = 110, 7\n", "\n", "# set the value of sample size and degrees of freedom\n", "n = 50\n", "k = n - 1\n", "\n", "# construct the confidence interval\n", "np.round(t.interval(0.95, df=k, loc=x_bar, scale=s / np.sqrt(n)), 2)" ] }, { "cell_type": "markdown", "metadata": { "id": "7dnKJdoTS3nb" }, "source": [ "#### Insight\n", "* 95% of the time, the mean caffeine content for cups of coffee dispensed by the machine will be between 108.01 mg and 111.99 mg." ] }, { "cell_type": "markdown", "metadata": { "id": "mesRClXhTWiL" }, "source": [ "#### Key Takeaways\n", "\n", "* The confidence interval for the population mean can be constructed for both cases when the population standard deviation is known and when it is unknown. The latter case is more common which demands the application of t-distribution with appropriate degrees of freedom.\n", "\n", "\n", "* The general approach to the construction of confidence interval is to use the appropriate sample statistic to estimate the population parameter and use the proper percentile point of the sampling distribution." ] }, { "cell_type": "markdown", "metadata": { "id": "HHhcxblrCPQs" }, "source": [ "\n", "# **Hypothesis Test for Population Mean $\\mu$**\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "imkkvBHLCr1p" }, "source": [ "### One Sample Z-test (when population standard deviation is known)\n", "\n", "It is rarely the case when you know the population standard deviation...but let's assume that is the case" ] }, { "cell_type": "markdown", "metadata": { "id": "JFYmMSXAD5r8" }, "source": [ "It is known from experience that for a certain E-commerce company the mean delivery time of the products is 5 days with a standard deviation of 1.3 days.\n", "\n", "The new customer service manager of the company is afraid that the company is slipping and collects a random sample of 45 orders. The mean delivery time of these samples comes out to be 5.25 days. \n", "\n", "Is there enough statistical evidence for the manager's apprehension that the mean delivery time of products is greater than 5 days.\n", "\n", "Use level of significance $\\alpha$ = 0.05" ] }, { "cell_type": "markdown", "metadata": { "id": "f5_ECLi6YZA2" }, "source": [ "### Let's write the null and alternate hypotheses" ] }, { "cell_type": "markdown", "metadata": { "id": "UjzLRZUjSLig" }, "source": [ "Let $\\mu$ be the mean delivery time of the products.\n", "\n", "The manager will test the null hypothesis\n", "\n", ">$H_0: \\mu = 5$\n", "\n", "against the alternate hypothesis\n", "\n", "> $H_a: \\mu > 5$" ] }, { "cell_type": "markdown", "metadata": { "id": "Za3CtsidYe2a" }, "source": [ "### Are the assumptions of Z-test satisfied?" ] }, { "cell_type": "markdown", "metadata": { "id": "uZEqFhp8V99Y" }, "source": [ "* Samples are drawn from a normal distribution - Since the sample size is 45(which is > 30), Central Limit Theorem states that the distribution of sample means will be normal. If the sample size was less than 30, we would have been able to apply z test on if we knew that the population distribution was normal. \n", "* Observations are from a simple random sample - we are informed that the manager collected a simple random sample\n", "* Standard deviation is known - Yes\n", "\n", "\n", "Voila! We can use Z-test for this problem." ] }, { "cell_type": "markdown", "metadata": { "id": "vI7uRPYSZDAv" }, "source": [ "### The next step is to find the Z test statistic\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "g03yfFvoV08J", "outputId": "e74f78eb-40ec-42fc-9cd8-4b4397036b84" }, "outputs": [ { "data": { "text/plain": [ "1.2900392177883402" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# set the values of population mean and population standard deviation to 5 and 1.3 respectively\n", "mu, sigma = 5, 1.3\n", "\n", "# set the value sample mean to 5.25\n", "x_bar = 5.25\n", "\n", "# calculate the test statistic\n", "test_stat = (x_bar - mu) / (sigma/np.sqrt(45))\n", "test_stat" ] }, { "cell_type": "markdown", "metadata": { "id": "ddz-nxAuaQl1" }, "source": [ "#### The Z test statistic follows a standard normal distribution.\n", "\n", "Let's plot the distribution of the Z test statistic and see where the computed test statistic lies in the plot." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "mKW-GHiZa6DE", "outputId": "3144c586-6dfe-4f89-f36e-7d0b76a91dfe" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# import the required function\n", "from scipy.stats import norm\n", "\n", "# plotting the distribution of Z test statistic along with the computed test statistic\n", "# We are plotting the distributions here to better visualize the calculations\n", "x = np.linspace(-4, 4, 100) # create an array of 100 numbers starting from -4 and ending at 4\n", "plt.plot(x, norm.pdf(x, 0, 1)) # plot the pdf of the normal distribution\n", "plt.axvline(x = test_stat, c = 'r') # draw a vertical red line through the mentioned point\n", "plt.show() # display the plot" ] }, { "cell_type": "markdown", "metadata": { "id": "2RoCBWfad8yi" }, "source": [ "What is the probability of getting the calculated value of test statistic or bigger in the above distribution?" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "P-sbsv2ued1d", "outputId": "341677f8-55b8-481f-a9ae-f4211e6fc012" }, "outputs": [ { "data": { "text/plain": [ "0.09851852092578695" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# calculate the probability using the cdf() function\n", "1 - norm.cdf(test_stat)" ] }, { "cell_type": "markdown", "metadata": { "id": "0b-uXxQZNS4e" }, "source": [ "**Though the probability is very small, is it significant enough to reject the null hypothesis in favor of alternate hypothesis?**" ] }, { "cell_type": "markdown", "metadata": { "id": "sVtMAHgbg1Ut" }, "source": [ "### Introduction of Rejection Acceptance Region/ p-value" ] }, { "cell_type": "markdown", "metadata": { "id": "xqqUout3gNK8" }, "source": [ "Though the probability is small, we can not conclude whether the evidence is significant enough to reject the null hypothesis in favor of alternate hypothesis or not. To determine it, we use either one of the following approaches:\n", "\n", "1- Rejection region approach\n", "\n", "2- p-value approach" ] }, { "cell_type": "markdown", "metadata": { "id": "4dihfsGeO-RR" }, "source": [ "#### Rejection Region Approach\n", "\n", "For this approach, we need to follow the below steps.\n", "\n", "\n", "1. We choose a value of level of significance ($\\alpha$).\n", "\n", " ($\\alpha$ is the probability of rejecting the null hypothesis if it is true.)\n", "\n", "2. Then, we find the rejection region in the graph.\n", "\n", "3. We reject the null hypothesis if the test statistic falls in the rejection region. Else, we don't reject the null hypothesis.\n", "\n", "In the given example, the Z test statistic follows a standard normal distribution as shown in the above plot. The Z values lying in the right end of the distribution gives strong evidence against the null hypothesis. To find the rejection region, we will find the value of Z (called critical value) that gives an area of $\\alpha$ to the right end." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "o_ITvMpZXLyI", "outputId": "4f262d0e-1caa-4a2e-8483-29db8a45b014" }, "outputs": [ { "data": { "text/plain": [ "1.6448536269514722" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# import the required function\n", "from scipy.stats import norm\n", "\n", "# find the critical value\n", "critical_val = norm.ppf(1-.05)\n", "critical_val" ] }, { "cell_type": "markdown", "metadata": { "id": "pj41yWnjYKZl" }, "source": [ "The critical value separates the region where we will reject the null hypothesis from the region where we won't reject the null hypothesis. See the below plot." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "3PUG_qdLYr64", "outputId": "84547a58-1659-469d-f8f3-418b45b8bcc1" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plotting the test statistic distribution and indicating the rejection and acceptance region\n", "# We are plotting the distributions here to better visualize the calculations\n", "x = np.linspace(-4, 4, 100) # create an array of 100 numbers starting from -4 and ending at 4\n", "plt.plot(x, norm.pdf(x, 0, 1)) # plot the pdf of the normal distribution\n", "plt.axvline(x = critical_val, c = 'r') # draw a vertical red line through the mentioned point\n", "x1 = np.linspace(critical_val, 4, 50) # create an array of 50 numbers starting from the critical value and ending at 4\n", "plt.fill_between(x1, norm.pdf(x1, 0, 1), color='r') # fill the area under the curve after the critical value with red color\n", "plt.annotate('Reject Null', (2, 0.20)) # annotate the mentioned text at the mentioned location\n", "plt.annotate(' Do Not Reject\\n Null', (-1, 0.20)) # annotate the mentioned text at the mentioned location\n", "plt.show() # display the plot" ] }, { "cell_type": "markdown", "metadata": { "id": "mhRuynC6bRcV" }, "source": [ "### Insight\n", "\n", "As our test statistic (~ 1.29) does not lie in the rejection region, we can not reject the null hypothesis. Thus, we do not have statistical evidence to say that the mean delivery time of a product is greater than 5 days." ] }, { "cell_type": "markdown", "metadata": { "id": "M__QsfhvzQdO" }, "source": [ "#### p-value Approach\n", "\n", "Though the rejection region approach gives us the desired conclusion, it does not say anything about the strength of the evidence. Hence, statisticians prefer p-value approach which measures the strength of the evidence against the null hypothesis.\n", "\n", "For this approach, we need to follow the below steps.\n", "\n", "1. We choose a level of significance ($\\alpha$)\n", "\n", "2. Then, we calculate the p-value.\n", "\n", "3. We reject the null hypothesis if p-value $\\leq \\alpha$. Else, we fail to reject the null hypothesis.\n", "\n", "The p-value is the probability of finding the observed test statistic or more extreme results, under the null hypothesis. \n", "\n", "In the given example, p-value is the area right to the test statistic under the standard normal curve.\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "au3_jODY1cYb", "outputId": "a29e8dcd-76a6-461b-91a3-d6f875597c4f" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plotting the test statistic distribution along with computed test statistic\n", "# We are plotting the distributions here to better visualize the calculations\n", "x = np.linspace(-4, 4, 100) # create an array of 100 numbers starting from -4 and ending at 4\n", "plt.plot(x, norm.pdf(x, 0, 1)) # plot the pdf of the normal distribution\n", "plt.axvline(x = test_stat, c = 'r') # draw a vertical red line through the mentioned point\n", "x1 = np.linspace(test_stat, 4, 50) # create an array of 50 numbers starting from the test statistic and ending at 4\n", "plt.fill_between(x1, norm.pdf(x1, 0, 1), color='r') # fill the area under the curve after the test statistic value with red color\n", "plt.show() # display the plot" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "Z6-VOxQqfOBF", "outputId": "cbfdfd12-beba-4c55-bbda-37bec6987ebf" }, "outputs": [ { "data": { "text/plain": [ "0.09851852092578695" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# calculate the p-value using the cdf() function\n", "1 - norm.cdf(test_stat)" ] }, { "cell_type": "markdown", "metadata": { "id": "3QCb1bK6gUTA" }, "source": [ "### Insight\n", "\n", "As the p-value ~0.098 is greater than level of significance, we can not reject the null hypothesis. Thus, we do not have statistical evidence to say that the mean delivery time of a product is greater than 5 days." ] }, { "cell_type": "markdown", "metadata": { "id": "noTA34C4hkyx" }, "source": [ "### Key Takeaway\n", "\n", "* We get the same result by using both the Rejection Region and p-value approach that the manager does not have enough statistical evidence to say that the mean delivery time of a product is greater than 5 days." ] }, { "cell_type": "markdown", "metadata": { "id": "POB5EwDV5vAS" }, "source": [ "# **One-tailed and Two-tailed Tests**" ] }, { "cell_type": "markdown", "metadata": { "id": "WiaDWDy1666u" }, "source": [ "### Let's see an example\n", "\n", "Suppose a soft-drink manufacturer's most selling product is 600 ml coke with a standard deviation of 50 ml.\n", "\n", "A customer would like to test whether there is at least 600 ml coke in the bottle. He doubts that the amount of coke in the bottle is less than 600 ml.\n", "\n", "The null hypothesis formed by the customer is\n", "\n", ">$H_0: \\mu = 600$\n", "\n", "against the alternative hypothesis\n", "\n", "> $H_a: \\mu < 600$\n", "\n", "However, the quality control team wants exactly 600 ml coke in the bottle. The team wants to ensure that the amount of coke in the bottle is not different from 600 ml.\n", "\n", "The null hypothesis formed by the quality control team is\n", "\n", ">$H_0: \\mu = 600$\n", "\n", "against the alternative hypothesis\n", "\n", "> $H_a: \\mu \\neq 600$\n", "\n", "Thus, the choice of one-sided vs two-sided alternative hypothesis depends on the nature of the problem." ] }, { "cell_type": "markdown", "metadata": { "id": "GWUkM0LrCzSu" }, "source": [ "### Two-tailed Test Example\n", "\n", "Suppose you work on the quality control team of the company. It is known from experience that the mean amount of coke in a bottle is 600 ml with a standard deviation of 50 ml.\n", "\n", "You have collected 36 randomly sampled bottles. The mean amount of coke in the 36 samples is 580 ml.\n", "\n", "You intend to test whether the amount of coke in the bottle is different from 600 ml using 0.05 level of significance. Do you have enough Statistical evidence for it?" ] }, { "cell_type": "markdown", "metadata": { "id": "kHPUcm3pryyd" }, "source": [ "### Are the assumptions of Z-test satisfied?" ] }, { "cell_type": "markdown", "metadata": { "id": "_NP5DlMXr2gR" }, "source": [ "* Samples are drawn from a normal distribution - Since the sample size is 36(which is > 30), Central Limit Theorem states that the distribution of sample means will be normal. If the sample size was less than 30, we would have been able to apply Z test on if we knew that the population distribution was normal. \n", "* Observations are from a simple random sample - we are informed that you have collected a simple random sample.\n", "* Standard deviation is known - Yes\n", "\n", "\n", "Voila! We can use Z-test for this problem." ] }, { "cell_type": "markdown", "metadata": { "id": "DouBcnk2siNr" }, "source": [ "### The next step is to find the test statistic" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "QZaRvsFXsqFm", "outputId": "cae555cc-7337-48be-9106-6f86a293899a" }, "outputs": [ { "data": { "text/plain": [ "-2.4" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# set the values of population mean and standard deviation to 600 and 50 respectively\n", "mu, sigma = 600, 50\n", "\n", "# set the value sample mean to 580\n", "x_bar = 580\n", "\n", "# calculate the test statistic\n", "test_stat = (x_bar - mu) / (sigma/np.sqrt(36))\n", "test_stat" ] }, { "cell_type": "markdown", "metadata": { "id": "z25Pi6HhtLNu" }, "source": [ "### Let's use the rejection region approach for two-tailed test\n", "\n", "In the given example, the Z test statistic follows a standard normal distribution. The Z values lying in the left and right end of the distribution gives strong evidence against the null hypothesis. To find the rejection region, we will find the values of Z (called critical values) that give an area of $\\alpha/2$ to both the left and right end." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "7PGKmNzjuolm", "outputId": "dd95a605-b753-4545-b65c-c756f2d05c82" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# import the required function\n", "from scipy.stats import norm\n", "\n", "# find the critical values\n", "critical_val1 = norm.ppf(1-(0.05/2))\n", "critical_val2 = norm.ppf(0.05/2)\n", "\n", "# plot the rejection and acceptance region\n", "# We are plotting the distributions here to better visualize the calculations\n", "x = np.linspace(-4, 4, 100) # create an array of 100 numbers starting from -4 and ending at 4\n", "plt.plot(x, norm.pdf(x, 0, 1)) # plot the pdf of the normal distribution\n", "plt.axvline(x = critical_val1, c = 'r') # draw a vertical red line through the mentioned point\n", "x1 = np.linspace(critical_val1, 4, 50) # create an array of 50 numbers starting from the critical value and ending at 4\n", "plt.fill_between(x1, norm.pdf(x1, 0, 1), color='r') # fill the area under the curve after the critical value with red color\n", "plt.axvline(x = critical_val2, c = 'r') # draw a vertical red line through the mentioned point\n", "x1 = np.linspace(-4, critical_val2, 50) # create an array of 50 numbers starting from -4 and ending at the critical value\n", "plt.fill_between(x1, norm.pdf(x1, 0, 1), color='r') # fill the area under the curve before the critical value with red color\n", "plt.annotate('Reject Null', (2.2, 0.20)) # annotate the mentioned text at the mentioned location\n", "plt.annotate('Reject Null', (-3.5, 0.20)) # annotate the mentioned text at the mentioned location\n", "plt.annotate(' Do Not Reject\\n Null', (-1, 0.20)) # annotate the mentioned text at the mentioned location\n", "plt.show() # display the plot" ] }, { "cell_type": "markdown", "metadata": { "id": "1x0cXahOwHE8" }, "source": [ "As our test statistic (~-2.4) lies in the rejection region, we can reject the null hypothesis. Thus, we have enough statistical evidence to say that the amount of coke in the bottle is different from 600 ml." ] }, { "cell_type": "markdown", "metadata": { "id": "9zzkUpjHPn_c" }, "source": [ "### One-tailed Test Example\n", "\n", "It is known that the mean amount of coke in a bottle is 600 ml with a standard deviation of 50 ml. Suppose you are a customer who wants to test whether the amount of coke in the bottle is less than 600 ml.\n", "\n", "You have collected 36 randomly sampled bottles. The mean amount of coke in the 36 samples is 580 ml.\n", "\n", "Do you have enough Statistical evidence for it?" ] }, { "cell_type": "markdown", "metadata": { "id": "vacq1cbrQH76" }, "source": [ "### Are the assumptions of Z-test satisfied?\n", "* Samples are drawn from a normal distribution - Since the sample size is 36(which is > 30), Central Limit Theorem states that the distribution of sample means will be normal. If the sample size was less than 30, we would have been able to apply Z test on if we knew that the population distribution was normal. \n", "* Observations are from a simple random sample - we are informed that you have collected a simple random sample.\n", "* Standard deviation is known - Yes\n", "\n", "\n", "Voila! We can use Z-test for this problem." ] }, { "cell_type": "markdown", "metadata": { "id": "9jeI1yRkRLN2" }, "source": [ "### The next step is to find the test statistic" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "8dZr5lGzRS7R", "outputId": "a0f0cce5-db02-49da-935e-cefa6e09ee52" }, "outputs": [ { "data": { "text/plain": [ "-2.4" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# set the values of population mean and standard deviation to 600 and 50 respectively\n", "mu, sigma = 600, 50\n", "\n", "# set the value sample mean to 580\n", "x_bar = 580\n", "\n", "# calculate the test statistic\n", "test_stat = (x_bar - mu) / (sigma/np.sqrt(36))\n", "test_stat" ] }, { "cell_type": "markdown", "metadata": { "id": "BUIBHwkPRPCQ" }, "source": [ "### Let's use the rejection region approach for one-tailed test\n", "\n", "In the given example, the Z test statistic follows a standard normal distribution. The Z values lying in the left end of the distribution gives strong evidence against the null hypothesis. To find the rejection region, we will find the value of Z (called critical value) that give an area of $\\alpha$ to both the left end." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "IhhNBBsuRjLI", "outputId": "19a188c4-a368-4525-ebb3-b61d45b393b8" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# import the required function\n", "from scipy.stats import norm\n", "\n", "# find the critical value\n", "critical_val = norm.ppf(0.05)\n", "\n", "# plot the rejection and acceptance region\n", "# We are plotting the distributions here to better visualize the calculations\n", "x = np.linspace(-4, 4, 100) # create an array of 100 numbers starting from -4 and ending at 4\n", "plt.plot(x, norm.pdf(x, 0, 1)) # plot the pdf of the normal distribution\n", "plt.axvline(x = critical_val, c = 'r') # draw a vertical red line through the mentioned point\n", "x1 = np.linspace(-4, critical_val, 50) # create an array of 50 numbers starting from -4 and ending at the critical value\n", "plt.fill_between(x1, norm.pdf(x1, 0, 1), color='r') # fill the area under the curve before the critical value with red color\n", "plt.annotate('Reject Null', (-3.5, 0.20)) # annotate the mentioned text at the mentioned location\n", "plt.annotate(' Do Not Reject\\n Null', (-1, 0.20)) # annotate the mentioned text at the mentioned location\n", "plt.show() # display the plot" ] }, { "cell_type": "markdown", "metadata": { "id": "fanaSBpeS0yQ" }, "source": [ "As our test statistic (~-2.4) lies in the rejection region, we can reject the null hypothesis. Thus, we have enough statistical evidence to say that the amount of coke in the bottle is less than from 600 ml." ] }, { "cell_type": "markdown", "metadata": { "id": "8Zf1FemQ4g9t" }, "source": [ "### Key Takeaways\n", "\n", "* In one-sided test, we consider the difference only in one direction. However, in two-sided tests we are interested to know the direction of the difference. \n", "* Depending on the nature of the problem choose one!" ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "Notebook Week2.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 1 }