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“Blood Pressure of Males and Females.” StatCruch, 2013. Available online at http://www.statcrunch.com/5.0/ viewreport.php?reportid=11960 (accessed May 14, 2013). “The Use of Epidemiological Tools in Conflict-affected populations: Open-access educational resources for policy-makers: Calculation of at http://conflict.ls... |
online at “Smart Phone Users, By The Numbers.” Visual.ly, 2013. Available online at http://visual.ly/smart-phone-users-numbers (accessed May 14, 2013). “Facebook Statistics.” Statistics Brain. Available online at http://www.statisticbrain.com/facebook-statistics/(accessed May 14, 2013). SOLUTIONS 1 ounces of water in ... |
.75)(14) = 149.5. 366 CHAPTER 6 | THE NORMAL DISTRIBUTION 67 Let X = an SAT math score and Y = an ACT math score. a. X = 720 720 – 520 = 1.74 The exam score of 720 is 1.74 standard deviations above the mean of 520. 15 b. z = 1.5 The math SAT score is 520 + 1.5(115) ≈ 692.5. The exam score of 692.5 is 1.5 standard devia... |
h. The answers to part f and part g are not exactly the same, because the normal distribution is only an approximation to the real one. i. The answers to part f and part g are close, because a normal distribution is an excellent approximation when the sample size is greater than 30. This content is available for free ... |
,54,48,5.5136) = 0.7641 b. For this problem: P(54 < x < 64) = normalcdf(54,64,48,5.5136) = 0.0018 c. For this problem: P(x > 64) = normalcdf(64,1099,48,5.5136) = 0.0000012 (approximately 0) 368 CHAPTER 6 | THE NORMAL DISTRIBUTION This content is available for free at http://textbookequity.org/introductory-statistics or... |
know it. The important fact is that the distribution of sample means and the sums tend to follow the normal distribution. The size of the sample, n, that is required in order to be "large enough" depends on the original population from which the samples are drawn (the sample size should be at least 30 or the data shou... |
distribution (the sampling distribution). 7.1 | The Central Limit Theorem for Sample Means (Averages) Suppose X is a random variable with a distribution that may be known or unknown (it can be any distribution). Using a subscript that matches the random variable, suppose: a. μX = the mean of X b. σX = the standard dev... |
size = n standard deviation sample size ⎞ ⎠ Example 7.1 An unknown distribution has a mean of 90 and a standard deviation of 15. Samples of size n = 25 are drawn randomly from the population. a. Find the probability that the sample mean is between 85 and 92. Solution 7.1 a. Let X = one value from the original unknown ... |
| THE CENTRAL LIMIT THEOREM 373 Example 7.2 The length of time, in hours, it takes an "over 40" group of people to play one soccer match is normally distributed with a mean of two hours and a standard deviation of 0.5 hours. A sample of size n = 50 is drawn randomly from the population. Find the probability that the s... |
the mean age of tablet users is 34 years. Suppose the standard deviation is 15 years. Take a sample of size n = 100. a. What are the mean and standard deviation for the sample mean ages of tablet users? b. What does the distribution look like? c. Find the probability that the sample mean age is more than 30 years (the... |
x¯ = µ = 8.2 σ x¯ = σ n = 1 60 = 0.13 b. This allows us to calculate the probability of sample means of a particular distance from the mean, in repeated samples of size 60. This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 7 | THE... |
following z-score associated with it: a. Σx is one sum. b. z = Σx – (n)(µ X) ( n)(σ X) i. ii. (n)(μX) = the mean of ΣX ( n)(σ X) = standard deviation of ΣX To find probabilities for sums on the calculator, follow these steps. 2nd DISTR 2:normalcdf normalcdf(lower value of the area, upper value of the area, (n)(mean), ... |
. Σx = (n)(μX) + (z) ( n) (σΧ) = (80)(90) + (1.5)( 80 )(15) = 7,401.2 This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 7 | THE CENTRAL LIMIT THEOREM 377 7.5 An unknown distribution has a mean of 45 and a standard deviation of eigh... |
. a. What are the mean and standard deviation for the sum of the ages of tablet users? What is the distribution? b. Find the probability that the sum of the ages is between 1,400 and 1,500 years. c. Find the 90th percentile for the sum of the 39 ages. 378 CHAPTER 7 | THE CENTRAL LIMIT THEOREM Example 7.7 The mean numbe... |
. Examples of the Central Limit Theorem Law of Large Numbers The law of large numbers says that if you take samples of larger and larger size from any population, then the mean x¯ of the sample tends to get closer and closer to μ. From the central limit theorem, we know that as n gets larger and larger, the sample mean... |
a. P( x¯ < 2) = 0 The probability that the mean stress score is less than two is about zero. Figure 7.4 normalcdf ⎛ ⎝1,2,3,1.15 75 ⎞ ⎠ = 0 380 CHAPTER 7 | THE CENTRAL LIMIT THEOREM REMINDER The smallest stress score is one. b. Find the 90th percentile for the mean of 75 stress scores. Draw a graph. Solution 7.8 b. Let... |
is about 237.8. This tells us that 90% of all the sums of 75 scores are no more than 237.8 and 10% are no less than 237.8. invNorm(0.90,(75)(3), ( 75) (1.15)) = 237.8 7.8 Use the information in Example 7.8, but use a sample size of 55 to answer the following questions. a. Find P( x¯ < 7). b. Find P(Σx > 170). c. Find ... |
.7919 that the mean excess time used is more than 20 minutes, for a sample of 80 customers who exceed their contracted time allowance. Figure 7.8 REMINDER 1E99 = 1099 and –1E99 = –1099. Press the EE key for E. Or just use 1099 instead of 1E99. b. Find P(x > 20). Remember to use the exponential distribution for an indiv... |
3,000). c. Find the 75th percentile for the sample mean excess time of 144 customers. d. Find the 85th percentile for the sum of 144 excess times used by customers. Example 7.10 In the United States, someone is sexually assaulted every two minutes, on average, according to a number of studies. Suppose the standard dev... |
6.74 7.10 Based on data from the National Health Survey, women between the ages of 18 and 24 have an average systolic blood pressures (in mm Hg) of 114.8 with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18 to 24 follow a normal distribution. a. b. c. If one woman from this popul... |
50. c. P(Σx ≥ 1,600) = normalcdf(1600,E99,1514.10,63) = 0.0864 d. P(Σx ≤ 1,595) = normalcdf(-E99,1595,1514.10,63) = 0.9005. This means that there is a 90% chance that the sum of the ages for the sample group n = 49 is at most 1595. e. The 95th percentile = invNorm(0.95,30.9,1.1) = 32.7. This indicates that 95% of the ... |
omial random variable, then X ~ B(n, p). The shape of the binomial distribution needs to be similar to the shape of the normal distribution. To ensure this, the quantities np and nq must both be greater than five (np > 5 and nq > 5; the approximation is better if they are both greater than or equal to 10). Then the bin... |
6447) = 0.5689 For part c, you exclude 155 so P(X > 155) has normal approximation P(y > 155.5) = 0.6572. normalcdf(155.5,10^99,159,8.6447) = 0.6572. For part d, you exclude 147 so P(X < 147) has normal approximation P(Y < 146.5) = 0.0741. normalcdf(0,146.5,159,8.6447) = 0.0741 For part e,P(X = 175) has normal approxima... |
Using the continuity correction factor, find the probability that at least 250 favor Dawn Morgan for mayor. This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 7 | THE CENTRAL LIMIT THEOREM 387 7.1 Central Limit Theorem (Pocket Chan... |
__________ __________ Table 7.2 3. Construct a histogram. Scale the axes using the same scaling you used for the section titled Collect the Data. Sketch the graph using a ruler and a pencil. Figure 7.11 4. Calculate the following (n = 2; surveying two people at a time): a. b. x¯ = _______ s = _______ 5. Draw a smooth c... |
~ _____(_____,_____) 4. In one to two complete sentences, explain any differences in your answers to the previous two questions. 390 CHAPTER 7 | THE CENTRAL LIMIT THEOREM 7.2 Central Limit Theorem (Cookie Recipes) Class Time: Names: Student Learning Outcomes • The student will demonstrate and compare properties of the... |
b. x¯ = ______ s x¯ = ______ 5. For the original population, construct a histogram. Make intervals with a bar width of one day. Sketch the graph using a ruler and pencil. Scale the axes. 392 CHAPTER 7 | THE CENTRAL LIMIT THEOREM Figure 7.13 6. Draw a smooth curve through the tops of the bars of the histogram. Use one ... |
sentences to explain what happened. 394 CHAPTER 7 | THE CENTRAL LIMIT THEOREM KEY TERMS Average a number that describes the central tendency of the data; there are a number of specialized averages, including the arithmetic mean, weighted mean, median, mode, and geometric mean. Central Limit Theorem sampling with size ... |
μ = 0 and σ = 1, the RV is called a standard normal distribution. Normal Distribution a continuous random variable (RV) with pdf f (x) = 1 σ 2π – (x – µ)2 2σ 2 e, where μ is the mean of the distribution and σ is the standard deviation.; notation: X ~ N(μ, σ). If μ = 0 and σ = 1, the RV is called the standard normal di... |
approximated by a normal distribution even if the original population is not normally distributed. Additionally, if the original population has a mean of μX and a standard deviation of σx, the mean of the sums is nμx and the standard deviation is ( n) (σx) where n is the sample size. 7.3 Using the Central Limit Theore... |
one review will take Yoonie from 3.5 to 4.25 hours. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability. 396 CHAPTER 7 | THE CENTRAL LIMIT THEOREM a. Figure 7.16 b. P(________ < x < ________) = _______ 4. Find the probability that the mean of a month’s reviews ... |
. Use the following information to answer the next six exercises: A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100. 16. Find the probability that the sum of the 100 values is greater than 3,910... |
, and a sample size of 100. Let X = one object of interest. 34. What is the mean of ΣX? 35. What is the standard deviation of ΣX? 398 CHAPTER 7 | THE CENTRAL LIMIT THEOREM 36. What is P(Σx > 9,000)? 7.3 Using the Central Limit Theorem Use the following information to answer the next ten exercises: A manufacturer produc... |
the following information to answer the next eight exercises: A uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken. 55. Find P(Σx > 420). 56. Find the 90th percentile for the sums. 57. Find the 15th percentile for the sums. 58. Find the first quartile for the sums. 59. Find the thi... |
hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36 taxpayers. a. b. In words, Χ = _____________ ¯ = _____________ In words, X ¯ ~ _____(_____,_____) c. X d. Would you be surprised if the 36 taxpayers finished their ... |
7 | THE CENTRAL LIMIT THEOREM ¯ b. When the sample size is large, X is approximately normally distributed. ¯ c. When the sample size is large, the standard deviation of X is approximately the same as the standard deviation of Χ. 68. The percent of fat calories that a person in America consumes each day is normally dis... |
��4.59, 16 0.10 ⎝4.59, 16 0.10 ¯ ~.2 The Central Limit Theorem for Sums 72. Which of the following is NOT TRUE about the theoretical distribution of sums? a. The mean, median and mode are equal. b. The area under the curve is one. c. The curve never touches the x-axis. d. The curve is skewed to the right. 73. Suppose t... |
If we surveyed 70 teachers instead of ten, graphically, how would that change the distribution in part d? If each of the 70 teachers received a $3,000 raise, graphically, how would that change the distribution in part b? 7.3 Using the Central Limit Theorem 76. The attention span of a two-year-old is exponentially dist... |
= -0.0005. Use bar widths of ten. h. Does this histogram look like the graph in part c? i. In one or two complete sentences, explain why the graphs either look the same or look different? j. Based upon the theory of the central limit theorem, X ¯ ~ _____(_____,____) Use the following information to answer the next thr... |
Find the probability that the average price for 30 gas stations is less than $4.55. a. 0.6554 b. 0.3446 c. 0.0142 d. 0.9858 e. 0 85. Suppose in a local Kindergarten through 12th grade (K - 12) school district, 53 percent of the population favor a charter school for grades K through five. A simple random sample of 300 ... |
the 30th percentile for the mean. e. P(56 < x¯ < 62) = _____ f. P(18 < x¯ < 58) = _____ g. Σx ~ _____(_____,_____) h. Find the minimum value for the upper quartile for the sum. i. P(1,400 < Σx < 1,550) = _____ 88. Suppose that the length of research papers is uniformly distributed from ten to 25 pages. We survey a cla... |
the hospital? Why or why not? Is it likely that the average stay for the 80 women was more than five days? Why or why not? i. An individual stayed more than five days. ii. the average stay of 80 women was more than five days. i. If we were to sum up the women’s stays, is it likely that, collectively they spent more th... |
0.859 0.784 0.824 0.858 0.848 0.851 0.696 0.876 0.855 0.806 0.840 0.868 0.859 0.982 0.881 0.925 0.863 0.914 0.775 0.881 0.854 0.865 0.810 0.865 0.858 1.015 0.818 0.876 0.868 0.809 0.803 0.865 0.932 0.848 0.842 0.940 0.832 0.833 0.807 0.845 0.841 0.852 0.932 0.778 0.833 0.814 0.881 0.791 0.818 0.810 0.864 0.881 0.825 0... |
42 0.758 0.757 0.724 0.757 0.744 0.738 0.763 0.756 0.760 0.768 0.761 0.742 0.734 0.754 0.758 0.735 0.740 0.743 0.737 0.737 0.725 0.761 0.758 0.756 Table 7.8 The screws were randomly selected from the local home repair store. a. Find the mean diameter and standard deviation for the sample b. Find the probability that 50... |
, 2013. Posted October 29, 2012. Available online at http://blog.flurry.com (accessed May 17, 2013). 7.3 Using the Central Limit Theorem Data from the Wall Street Journal. “National Health and Nutrition Examination Survey.” Center for Disease Control and Prevention. Available online at http://www.cdc.gov/nchs/nhanes.ht... |
b. mean length of time for a sample of 36 taxpayers to complete IRS form 1040, in hours. c. N ⎛ ⎝10.53, 1 3 ⎞ ⎠ d. Yes. I would be surprised, because the probability is almost 0. e. No. I would not be totally surprised because the probability is 0.2312 65 a. the length of a song, in minutes, in the collection b. U(2, ... |
be more spread out. It would be a more symmetrical normal curve. i. If every teacher received a $3,000 raise, the distribution of X would shift to the right by $3,000. In other words, it would have a mean of $47,000. 77 a. X = the closing stock prices for U.S. semiconductor manufacturers c. b. i. $20.71; ii. $17.31; i... |
Σ x¯ = 85.65, Σs = 5.18 c. normalcdf(396.9,E99,(465)(0.8565),(0.05)( 465 )) ≈ 1 d. Since the probability of a sample of size 465 having at least a mean sum of 396.9 is appproximately 1, we can conclude that Mars is correctly labeling their M&M packages. 95 Use normalcdf ⎛ ⎝E – 99,1.1,1, 1 70 ⎞ ⎠ = 0.7986. This means t... |
you are trying to determine the percentage of times you make a basket when shooting a basketball, you might count the number of shots you make and divide that by the number of shots you attempted. In this case, you would have obtained a point estimate for the true proportion. 412 CHAPTER 8 | CONFIDENCE INTERVALS We us... |
mean x¯ is likely to be within 0.2 units of μ. is within 0.2 units of μ, which is unknown, then μ is likely to be within 0.2 units of x¯ Because x¯ in 95% of the samples. The population mean μ is contained in an interval whose lower number is calculated by taking the sample mean and subtracting two standard deviations... |
your class eats out in a week. Assume that the standard deviation is known to be three meals. Construct an approximate 95% confidence interval for the true mean number of meals students eat out each week. 1. Calculate the sample mean. 2. Let σ = 3 and n = the number of students surveyed. 3. Construct the interval ⎛ ⎛ ... |
a sample. We know the sample mean but we do not know the mean for the entire population. The sample mean is seven, and the error bound for the mean is 2.5. x¯ = 7 and EBM = 2.5 The confidence interval is (7 – 2.5, 7 + 2.5), and calculating the values gives (4.5, 9.5). If the confidence level (CL) is 95%, then we say t... |
distribution to calculate the error bound. Calculating the Confidence Interval To construct a confidence interval estimate for an unknown population mean, we need data from a random sample. The steps to construct and interpret the confidence interval are: • Calculate the sample mean x¯ standard deviation σ. from the s... |
(0, 1). Calculating the Error Bound (EBM) The error bound formula for an unknown population mean μ when the population standard deviation σ is known is • EBM = ⎛ ⎝z α 2 ⎞ ⎛ ⎝ ⎠ σ n ⎞ ⎠ Constructing the Confidence Interval • The confidence interval estimate has the format ( x¯ – EBM, x¯ + EBM). The graph gives a picture... |
be found using appropriate commands on other calculators, using a computer, or using a probability table for the standard normal distribution. EBM = (1.645) ⎛ ⎝ ⎞ ⎠ 3 36 = 0.8225 x¯ - EBM = 68 - 0.8225 = 67.1775 x¯ + EBM = 68 + 0.8225 = 68.8225 The 90% confidence interval is (67.1775, 68.8225). Solution 8.2 Solution B... |
Phone Model Apple iPhone 4S 1.11 LG Ally BlackBerry Pearl 8120 1.48 LG AX275 BlackBerry Tour 9630 1.43 LG Cosmos Cricket TXTM8 1.3 LG CU515 HP/Palm Centro 1.09 LG Trax CU575 HTC One V 0.455 Motorola Q9h 1.36 1.34 1.18 1.3 1.26 1.29 Pantech Laser Samsung Character Samsung Epic 4G Touch Samsung M240 Samsung Messager III... |
is between 0.8809 and 1.1671 watts per kilogram. Solution 8.3 Solution B Press STAT and arrow over to TESTS. Arrow down to 7:ZInterval. Press ENTER. Arrow to Stats and press ENTER. Arrow down and enter the following values: σ: 0.337 x¯ : 1.024 n: 30 C-level: 0.98 Arrow down to Calculate and press ENTER. The confidence... |
find the confidence interval, you need the sample mean, x¯, and the EBM. x¯ = 68 EBM = ⎛ ⎝; n = 36; The confidence level is 95% (CL = 0.95). CL = 0.95 so α = 1 – CL = 1 – 0.95 = 0.05 α 2 = 0.025 z α 2 = z0.025 The area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 – 0.025 = 0.975. = z0.025 = ... |
deliver time is 36 minutes. Use a sample size of 20. Find a 95% confidence interval estimate for the true mean pizza delivery time. Example 8.5 Suppose we change the original problem in Example 8.2 to see what happens to the error bound if the sample size is changed. Leave everything the same except the sample size. U... |
. Finding the Error Bound • From the upper value for the interval, subtract the sample mean, • OR, from the upper value for the interval, subtract the lower value. Then divide the difference by two. Finding the Sample Mean • Subtract the error bound from the upper value of the confidence interval, • OR, average the upp... |
population mean age of Foothill College students, how many randomly selected Foothill College students must be surveyed? From the problem, we know that σ = 15 and EBM = 2. z = z0.025 = 1.96, because the confidence level is 95%. n = z2 σ 2 EBM 2 = (1.96)2 (15)2 22 = 216.09 using the sample size equation. Use n = 217: A... |
30. With graphing calculators and computers, the practice now is to use the Student's t-distribution whenever s is used as an estimate for σ. If you draw a simple random sample of size n from a population that has an approximately a normal distribution with mean μ and unknown population standard deviation σ and calcul... |
and 84+ have a tcdf function to find the probability for given values of t. The grammar for the tcdf command is tcdf(lower bound, upper bound, degrees of freedom). However for confidence intervals, we need to use inverse probability to find the value of t when we know the probability. For the TI-84+ you can use the in... |
is: ( x¯ − EBM, x¯ + EBM). To calculate the confidence interval directly: Press STAT. Arrow over to TESTS. Arrow down to 8:TInterval and press ENTER (or just press 8). Example 8.8 Suppose you do a study of acupuncture to determine how effective it is in relieving pain. You measure sensory rates for 15 subjects with th... |
30 and 9.15. Solution 8.8 This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 8 | CONFIDENCE INTERVALS 425 Press STAT and arrow over to TESTS. Arrow down to 8:TInterval and press ENTER (or you can just press 8). Arrow to Data and pre... |
156 94 121 144 123 114 139 99 Table 8.3 Use this sample data to construct a 90% confidence interval for the mean number of targeted industrial chemicals to be found in an in infant’s blood. Solution 8.9 Solution A 426 CHAPTER 8 | CONFIDENCE INTERVALS From the sample, you can calculate x¯ = 127.45 and s = 25.965. There... |
.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 8 | CONFIDENCE INTERVALS 427 8.3 | A Population Proportion During an election year, we see articles in the newspaper that state confidence intervals in terms of proportions or percentages. For example, a poll for a particular candidate runn... |
�� X ⎝ npq n np n, ⎞ ⎠ Using algebra to simplify : npq n = pq n P′ follows a normal distribution for proportions: X n = P′ ~ N⎛ ⎝ np n, npq n ⎞ ⎠ The confidence interval has the form (p′ – EBP, p′ + EBP). EBP is error bound for the proportion. p′ = x n p′ = the estimated proportion of successes (p′ is a point estimate ... |
in a large city who have cell phones. Five hundred randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes - they own cell phones. Using a 95% confidence level, compute a confidence interval estimate for the true proportion o... |
% of all adult residents of this city have cell phones. Explanation of 95% Confidence Level Ninety-five percent of the confidence intervals constructed in this way would contain the true value for the population proportion of all adult residents of this city who have cell phones. Solution 8.10 Solution B Press STAT and... |
645) (0.60)(0.40) 500 = 0.036 p′ – EBP = 0.60 − 0.036 = 0.564 p′ + EBP = 0.60 + 0.036 = 0.636 The confidence interval for the true binomial population proportion is (p′ – EBP, p′ + EBP) = (0.564,0.636). Interpretation • We estimate with 90% confidence that the true percent of all students that are registered voters is ... |
simple adjustment that allows us to produce more accurate confidence intervals. We simply pretend that we have four additional observations. Two of these observations are successes and two are failures. The new sample size, then, is n + 4, and the new count of successes is x + 2. Computer studies have demonstrated the... |
ENTER. The confidence interval is (0.113, 0.439). 8.12 Out of a random sample of 65 freshmen at State University, 31 students have declared a major. Use the “plusfour” method to find a 96% confidence interval for the true proportion of freshmen at State University who have declared a major. Example 8.13 The Berkman Ce... |
to teens in smaller focus groups, but also interviewed additional teens over the phone. When the study was complete, 588 teens had answered the question about their Facebook friends with 159 saying that they have more than 500 friends. Use the “plus-four” method to find a 90% confidence interval for the true proportio... |
points of the true population proportion. To calculate the sample size n, use the formula and make the substitutions. n = z2 p′ q′ EBP2 gives n = 1.6452(0.5)(0.5) 0.032 = 751.7 Round the answer to the next higher value. The sample size should be 752 cell phone customers aged 50+ in order to be 90% confident that the e... |
variable X 3. State the estimated distribution to use. Use both words and symbols. Find the Confidence Interval 1. Calculate the confidence interval and the error bound. a. Confidence Interval: _____ b. Error Bound: _____ 436 CHAPTER 8 | CONFIDENCE INTERVALS 2. How much area is in both tails (combined)? α = _____ 3. H... |
____________ 2. In words, define the random variable P′. 3. State the estimated distribution to use. Find the Confidence Interval and Error Bound 1. Calculate the confidence interval and the error bound. a. Confidence Interval: _____ b. Error Bound: _____ 2. How much area is in both tails (combined)? α = _____ 3. How m... |
.3 62.9 60.6 63.8 58.8 64.9 65.7 62.5 70.9 62.9 63.1 62.2 58.7 64.7 66.0 60.5 64.7 65.4 60.2 65.0 64.1 61.1 65.3 64.6 59.2 61.4 62.0 63.5 61.4 65.5 62.3 65.5 64.7 58.8 66.1 64.9 66.9 57.9 69.8 58.5 63.4 69.2 65.9 62.2 60.0 58.1 62.5 62.4 59.1 66.4 61.2 60.4 58.7 66.7 67.5 63.2 56.6 67.7 62.5 Table 8.8 Heights of 100 Wo... |
of the confidence interval? 2. Divide this number by the total number of confidence intervals generated by the class to determine the percent of confidence intervals that contains the mean μ. Write this percent here: _____________. 3. Is the percent of confidence intervals that contain the population mean μ close to 9... |
Confidence Interval (CI) an interval estimate for an unknown population parameter. This depends on: • • • the desired confidence level, information that is known about the distribution (for example, known standard deviation), the sample and its size. Confidence Level (CL) the percent expression for the probability tha... |
than the number of data. CHAPTER REVIEW 8.1 A Single Population Mean using the Normal Distribution In this module, we learned how to calculate the confidence interval for a single population mean where the population standard deviation is known. When estimating a population mean, the margin of error is called the erro... |
confidence interval under this distribution is calculated with EBM = ⎛ ⎝t α 2 where t α 2, s is the sample is the t-score with area to the right equal to α 2 for a given α. standard deviation, and n is the sample size. Use a table, calculator, or computer to find t α 2 s n ⎞ ⎠ 8.3 A Population Proportion Some statisti... |
EBM) = ( x¯ − EBM, x¯ + EBM) = ⎛ n, x¯ + z σ n ⎞ ⎠ ⎝ x¯ − z σ EBM = z σ n = the error bound for the mean, or the margin of error for a single population mean; this formula is used when the population standard deviation is known. CL = confidence level, or the proportion of confidence intervals created that are expected... |
2 Single Population Mean, Known Standard Deviation, Normal Distribution Use the Normal Distribution for Means, Population Standard Deviation is Known EBM = z α 2 σ n ⋅ The confidence interval has the format ( x¯ − EBM, x¯ + EBM). 8.2 A Single Population Mean using the Student t Distribution s = the standard deviation ... |
sketch the graph, and calculate the error bound. 5. What will happen to the confidence interval obtained, if 500 newborn elephants are weighed instead of 50? Why? Use the following information to answer the next seven exercises: The U.S. Census Bureau conducts a study to determine the time needed to complete the short... |
20. In complete sentences, give an interpretation of what the interval in Exercise 8.18 means. 21. What would happen if 40 heads of lettuce were sampled instead of 20, and the error bound remained the same? 22. What would happen if 40 heads of lettuce were sampled instead of 20, and the confidence level remained the s... |
answer the next five exercises. A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 70 patients. The sample mean was 1.5 hours with a sample standard deviation of 0... |
your answer to Exercise 8.52, state the exact distribution to use when calculating the confidence interval. Construct a 95% confidence interval for the true mean number of colors on national flags. This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col1... |
decisions. State the confidence interval, sketch the graph, and calculate the error bound. 68. List two difficulties the company might have in obtaining random results, if this survey were done by email. Use the following information to answer the next five exercises: Of 1,050 randomly selected adults, 360 identified ... |
, define the random variable X. 81. Calculate the following: a. x = _______ b. n = _______ c. p′ = _______ 82. State the estimated distribution of X. X~________ 83. Define a new random variable P′. What is p′ estimating? 84. In words, define the random variable P′. 85. State the estimated distribution of P′. Construct ... |
the graph. iii. Calculate the error bound. e. What will happen to the level of confidence obtained if 1,000 male Swedes are surveyed instead of 48? Why? 96. Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.94 da... |
words, define the random variable X. ¯. In words, define the random variable X c. d. Which distribution should you use for this problem? Explain your choice. e. Construct a 90% confidence interval for the population mean weight of the candies. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the ... |
each election cycle. During the 2012 campaign season, there were 1,619 candidates for the House of Representatives across the United States who received contributions from individuals. Table 8.11 shows the total receipts from individuals for a random selection of 40 House candidates rounded to the nearest $100. The st... |
number of snack pieces in the six bags was 68. We wish to calculate a 96% confidence interval for the population proportion of Bam-Bam snack pieces. a. Define the random variables X and P′ in words. b. Which distribution should you use for this problem? Explain your choice c. Calculate p′. d. Construct a 96% confidenc... |
a sample standard deviation of four hours. a. i. ii. x¯ = __________ s x = __________ iii. n = __________ iv. n – 1 = __________ ¯ b. Define the random variables X and X c. Which distribution should you use for this problem? Explain your choice. d. Construct a 95% confidence interval for the population mean time waste... |
Calculate the error bound. f. Why would the error bound change if the confidence level were lowered to 90%? This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 109. The Federal Election Commission (FEC) collects information about campaign c... |
63 53 50 59 60 60 57 46 55 63 57 47 55 57 43 61 62 49 67 67 55 55 49 Table 8.13 Use this sample data to construct a 90% confidence interval for the mean age of CEO’s for these top small firms. Use the Student's t-distribution. 111. Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wan... |
to the store and record the grams of fat per serving of six brands of chocolate chip cookies. d. Calculate the mean. e. Is the mean within the interval you calculated in part a? Did you expect it to be? Why or why not? 114. A survey of the mean number of cents off that coupons give was conducted by randomly surveying ... |
determine this population proportion, what is the minimum number you would need b. to survey to be 95% confident that the population proportion is estimated to within 0.03? If it were later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minim... |
use for this problem? Explain your choice. c. Construct a 95% confidence interval. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. 121. Refer to the information in Exercise 8.120. a. Construct three 95% confidence intervals. i. percent of all Asians who would welcome a white per... |
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