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of Hispanic students at Cabrillo College and Lake Tahoe College are different. 103 a 105 Test: two independent sample proportions. Random variable: p′1 - p′2 Distribution: H0: p1 = p2 Ha: p1 ≠ p2 The proportion of e-reader users is different for the 16- to 29-year-old users from that of the 30 and older users. Graph: ... |
82 f. p-value: zero g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reject the null hypothesis. iii. Reason for Decision: p-value < alpha iv. Conclusion: At the 5 percent significance level, there is sufficient evidence to conclude that the proportions of males and females with at least one pierced ear is ... |
2.4, ¯ 1.8} Random Variable: X in the northeastern states between 2012 and 2011 is less than zero. The underemployment rate went down from 2011 to 2012. Graph: left-tailed. Distribution: H0: μd = 0 Ha: μd < 0 The mean of the differences of the rate of underemployment d Figure 10.24 636 Chapter 10 | Hypothesis Testing w... |
in the lottery example • The test of independence, which determines if events are independent, such as in the movie example • The test of a single variance, which tests variability, such as in the coffee example NOTE Though the chi-square distribution depends on calculators or computers for most of the calculations, t... |
peak. Figure 11.3 11.2 | Goodness-of-Fit Test In this type of hypothesis test, you determine whether the data fit a particular distribution. For example, you may suspect your unknown data fit a binomial distribution. You use a chi-square test, meaning the distribution for the hypothesis test is chi-square, to determin... |
perception. a. Can you use the information as it appears in the charts to conduct the goodness-of-fit test? Solution 11.1 a. No. Notice that the expected number of absences for the 12+ entry is less than five; it is two. Combine that group with the 9–11 group to create new tables where the number of students for each ... |
9 9 15 Table 11.7 Day of the Week Employees Were Most Absent Solution 11.2 The null and alternative hypotheses are as follows: • H0: The absent days occur with equal frequencies; that is, they fit a uniform distribution. • Ha: The absent days occur with unequal frequencies; that is, they do not fit a uniform distribut... |
. The next example, Example 11.3, has the calculator instructions. The newer TI-84 calculators have in STAT TESTS the test Chi2 GOF. To run the test, put the observed values—the data—into a first list and the expected values—the values you expect if the null hypothesis is true—into a second list. Press STAT TESTS and C... |
population as a whole? Solution 11.3 This problem asks you to test whether the far western U.S. families distribution fits the distribution of the American families. This test is always right-tailed. The first table contains expected percentages. To get expected (E) frequencies, multiply the percentage by 600. The exp... |
in them—see the note at the end of Example 11.2. Into L1, put the observed frequencies 66, 119, 349, 60, 15. Into L2, put the expected frequencies.10*600,.16*600,.55*600,.11*600,.08*600. Arrow over to list L3 and up to the name area L3. Enter (L1-L2)^2/L2 and ENTER. Press 2nd QUIT. Press 2nd LIST and arrow over to MAT... |
11.4 This problem can be set up as a goodness-of-fit problem. The sample space for flipping two fair coins is {HH, HT, TH, TT}. Out of 100 flips, you would expect 25 HH, 25 HT, 25 TH, and 25 TT. This is the expected distribution. The question, “Are the coins fair?” is the same as saying, “Does the distribution of the ... |
Rounded to two decimal places, you should see 2.14. Press 2nd DISTR. Arrow down to 7:χ2cdf—or press 7. Press ENTER. Enter 2.14,1E99,2). Rounded to four places, you should see.3430, which is the p-value. The newer TI-84 calculators have in STAT TESTS the test Chi2 GOF. To run the test, put the observed values—the data—... |
P(B). A AND B is the event that a driver received a speeding violation last year and also used a cell phone while driving. Suppose, in a study of drivers who received speeding violations in the last year, and who used cell phones while driving, that 755 people were surveyed. Out of the 755, 70 had a speeding violation ... |
cnx.org/content/col30309/1.8 Chapter 11 | The Chi-Square Distribution 651 Example 11.6 In a volunteer group, adults 21 and older volunteer from one to nine hours each week to spend time with a disabled senior citizen. The program recruits among community college students, four-year college students, and non-students. I... |
assume α = 0.05. p-value = 0.0113. α > p-value. Make a decision: Since α > p-value, reject H0. This means that the factors are not independent. Conclusion: At a 5 percent level of significance, from the data, there is sufficient evidence to conclude that the number of hours volunteered and the type of volunteer are de... |
freedom. Example 11.7 De Anza College is interested in the relationship between anxiety level and the need to succeed in school. A random sample of 400 students took a test that measured anxiety level and need to succeed in school. Table 11.18 shows the results. De Anza College wants to know if anxiety level and need ... |
populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. NOTE The expected value for each cell needs to be at least five for you to use this test. Hypotheses H0: The distributions of the two populations are the same.... |
-TEST. Press ENTER. You should see Observed:[A] and Expected:[B]. Arrow down to Calculate. Press ENTER. The test statistic is 10.1287 and the p-value = 0.0175. Do the procedure a second time but arrow down to Draw instead of Calculate. Compare α and the p-value: Since no α is given, assume α = 0.05. p-value = 0.0175. α... |
= 0.1959 Press the MATRX key and arrow over to EDIT. Press 1:[A]. Press 2 ENTER 3 ENTER. Enter the table values by row. Press ENTER after each. Press 2nd QUIT. Press STAT and arrow over to TESTS. Arrow down to C:χ2-TEST. Press ENTER. You should see Observed:[A] and Expected:[B]. Arrow down to Calculate. Press ENTER. T... |
(all outcomes occur with equal frequency), the population is normal, or the population is the same as another population with a known distribution. The null and alternative hypotheses are as follows: H0: The population fits the given distribution. Ha: The population does not fit the given distribution. Independence: U... |
are given the population standard deviation, we can set up the test using the population variance as follows: • H0: σ2 = 52 • Ha: σ2 > 52 11.10 A scuba instructor wants to record the collective depths each of his students dives during their checkout. He is interested in how the depths vary, even though everyone should... |
α > p-value, reject H0. This means that you reject σ2 = 7.22. In other words, you do not think the variation in waiting times is 7.2 minutes; you think the variation in waiting times is less. Conclusion: At a 5 percent level of significance, from the data, there is sufficient evidence to conclude that a single line ca... |
__________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ Table 11.23 2. Construct a histogram of the data. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes. Figure 11.9 3. Cal... |
determine the expected number of receipts and record that. Cell Observed Expected 1st 2nd 3rd 4th 5th 6th Table 11.25 4. H0: ________ 664 Chapter 11 | The Chi-Square Distribution 5. Ha: ________ 6. What distribution should you use for a hypothesis test? 7. Why did you choose this distribution? 8. Calculate the test st... |
1. Is the conclusion of your study the same as or different from your answer to answer to Question 2 under Collect the Data? 2. Why do you think that occurred? This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 11 | The Chi-Square Distribution 667 KEY TERMS contingency table a tabl... |
which need not be known, you can apply the test for homogeneity that uses the chi-square distribution. The null hypothesis for this test states that the populations of the two data sets come from the same distribution. The test compares the observed values against the expected values if the two populations followed th... |
)2 E • The test statistic is Σ (i ⋅ j) observed values, E = expected values, i = the number of rows in the table, and j = the number of columns in the table. where O = • If the null hypothesis is true, the expected number E = (row total)(column total) total surveyed. PRACTICE 11.1 Facts About the Chi-Square Distributio... |
she goes along, she records the actual maximum weights her clients lifted. She wants to know how well her expectations met with what was observed. Use the following information to answer the next five exercises. A teacher predicts the distribution of grades on the final exam. The predictions are shown in Table 11.27. ... |
.05. Decision: ________________ Reason for the decision: ________________ Conclusion (write out in complete sentences): ________________ 22. Does it appear that the pattern of disease cases in Santa Clara County corresponds to the distribution of ethnic groups in this county? Why or why not? 11.3 Test of Independence D... |
886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 whites. Of the people using the product 11 to 20 times per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people using the product 21 to... |
have the same distribution of sales throughout the year. What type of test should he use? 46. A meteorologist wants to know if East and West Australia have the same distribution of storms. What type of test should she use? 47. What condition must be met to use the test for homogeneity? Use the following information to... |
________ Use the following information to answer the next four exercises: The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctor’s office has a standard deviation of waiting times of 4.1 minutes. One... |
Married Widowed 140 238 2 Divorced/Separated 20 Table 11.36 Use the following information to answer the next two exercises. The columns in Table 11.37 contain the Race/Ethnicity of U.S. Public Schools for a recent year, the percentages for the Advanced Placement Examinee Population for that class, and the Overall Stud... |
. The second column in each table does not add to 100 percent because of rounding. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 11 | The Chi-Square Distribution 677 77. Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distr... |
the number of businesses in each category that recycle one commodity. Based on the study, on average half of the businesses were expected to be recycling one commodity. As a result, the last column shows the expected number of businesses in each category that recycle one commodity. At the 5 percent significance level,... |
individual drives and the number of people in the driver’s family—that is, whether car size and family size are independent. To test this, suppose that 800 car owners were randomly surveyed with the results in Table 11.44. Conduct a test of independence. Family Size Sub & Compact Mid-Size Full-Size Van & Truck 1 2 3–4... |
insurance agent in the Buffalo, New York area, the following is a breakdown of the amount of life insurance purchased by males in the following age groups. He is interested in whether the age of the male and the amount of life insurance purchased are independent events. Conduct a test for independence. Age of Males No... |
11.52 provides results of a recent survey of the youngest online entrepreneurs whose net worth is estimated at one million dollars or more. Their ages range from 17 to 30. Each cell in the table illustrates the number of entrepreneurs who correspond to the specific age group and their net worth. Are the ages and net w... |
Of the 293 randomly selected fish caught in Echo Lake, 115 were rainbow trout, 58 were other trout, 67 were bass, and 53 were catfish. Perform a test for homogeneity at a 5 percent level of significance. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 11 | The Chi-Square Distrib... |
Chi-Square Distribution 106. The Insurance Institute for Highway Safety collects safety information about all types of cars every year and publishes a report of top safety picks among all cars, makes, and models. Table 11.58 presents the number of top safety picks in six car categories for the two years 2009 and 2013.... |
. chi-square test statistic = ________ 115. p-value = ________ 116. Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade the p-value. 117. Let α = 0.05 Decision: ________ Conclusion (write out in a complete sentence): ________ 118. How did you know to test the variance inste... |
with a sample standard deviation of 3.9. Conduct a hypothesis test of the airline executive’s belief. 125. The number of births per woman in China is 1.6, down from 5.91 in 1966. This fertility rate has been attributed to the law passed in 1979 restricting births to one per woman. Suppose that a group of students stud... |
apples. Class A apples have a mean weight of 150 grams, and there is a maximum allowed weight tolerance of 5 percent above or below the mean for apples in the same consumer package. A batch of apples is selected to be included in a Class A apple package. Given the following apple weights of the batch, does the fruit c... |
/cprs.html U.S. Census Bureau. (n.d). Retrieved from https://www.census.gov/ 11.3 Test of Independence Harris Interactive. (n.d.). Retrieved from http://www.statisticbrain.com/favorite-flavor-of-ice-cream/ Statistics Brain. (2016, June 29). Youngest online entrepreneurs list. Retrieved from http://www.statisticbrain.co... |
s solution. Decision: Reject the null hypothesis. Reason for decision: p-value < alpha Conclusion: The make-up of cases does not fit the ethnicities of the general population of Santa Clara County. 23 a test of independence 25 a test of independence 27 8 29 6.6 31 0.0435 33 Product-use Per Day African American Native H... |
Ha: σ2 > 0.812 65 a test of a single variance 67 0.0542 69 true 71 false 73 Marital Status % Expected Frequency Never Married 31.3% 125.2 Married Widowed 56.1% 224.4 2.5% 10 Divorced/Separated 10.1% 40.4 Table 11.62 a. The data fit the distribution. This OpenStax book is available for free at http://cnx.org/content/co... |
alpha iv. Conclusion: There is insufficient evidence to conclude that the distribution of actual college majors of graduating females do not fit the distribution of their expected majors. 79 true 81 true 83 false Chapter 11 | The Chi-Square Distribution 690 85 a. H0: Surveyed individuals fit the distribution of expect... |
location. c. df = 6 d. chi-square distribution with df = 6 e. test statistic =18.8369 f. p-value = 0.0044 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reject the null hypothesis. iii. Reason for decision: p-value < alpha iv. Conclusion: At the 5 percent significance level, there is sufficient evidence ... |
same in Green Valley Lake and in Echo Lake. b. Ha: The distribution for fish caught is not the same in Green Valley Lake and in Echo Lake. c. 3 d. chi-square with df = 3 e. 11.75 f. p-value = 0.0083 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reject the null hypothesis. iii. Reason for decision: p-val... |
distribution 122 a. H0: σ = 15 b. Ha: σ > 15 c. df = 42 d. chi-square with df = 42 e. test statistic = 26.88 f. p-value = 0.9663 g. Check student’s solution. h. i. Alpha = 0.05 ii. Decision: Do not reject null hypothesis. iii. Reason for decision: p-value > alpha iv. Conclusion: There is insufficient evidence to concl... |
The test statistic is always positive and if the expected and observed values are not close together, the test statistic is large and the null hypothesis will be rejected. b. Testing to see if the data fits the distribution too well or is too perfect. This OpenStax book is available for free at http://cnx.org/content/... |
x The graph of a linear equation of the form y = a + bx is a straight line. Any line that is not vertical can be described by this equation. Example 12.2 Graph the equation y = –1 + 2x. Figure 12.2 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 12 | Linear Regression and Correla... |
Linear Regression and Correlation Figure 12.4 Three possible graphs of y = a + bx. (a) If b > 0, the line slopes upward to the right. (b) If b = 0, the line is horizontal. (c) If b < 0, the line slopes downward to the right. Example 12.4 Svetlana tutors to make extra money for college. For each tutoring session, she c... |
ruler. Then, by eye, draw a line that appears to fit the data. For your line, pick two convenient points and use them to find the slope of the line. Find the y-intercept of the line by extending your line so it crosses the y-axis. Using the slopes and the y-intercepts, write your equation of best fit. Do you think eve... |
from Example 12.5 after the ordered pairs have been listed by ordering x values. If multiple data points have the same y values, then they are listed in order from least to greatest y (see data values where x = 71). We first divide our scores into three groups of approximately equal numbers of x values per group. The ... |
1 x2 − x1. Substituting the median x and y values from the first and third groups gives m = 174 − 143 71 − 66.5, which simplifies to m ≈ 6.9. The y-intercept may be found using the formula b = Σy − mΣx 3, which means the quantity of the sum of the median y values minus the slope times the sum of the median x values div... |
line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative and the line overestimates that actual data value for y. In Figure 12.6, y0 – ŷ0 = ε0 is the residual for the point shown. Here the point lies above the line and the residual is positive. ε = the G... |
the data are scattered about a straight line. To find that line, we minimize the sum of the squared errors (SSE), or make it as small as possible. Any other line you might choose would have a higher SSE than the best-fit line. This best-fit line is called the least-squares regression line. NOTE Computer spreadsheets, ... |
measured by the absorbance reading. Table 12.5 shows the expected absorbance readings at different protein concentrations. This is called a standard curve for the assay. Concentration (mM) Absorbance (mAU) 125 250 500 750 1,000 1,500 2,000 Table 12.5 0.021 0.023 0.068 0.086 0.105 0.124 0.146 The scatter plot Figure 12... |
3. On the LinRegTTest input screen, enter Xlist: L1, Ylist: L2, and Freq: 1. 4. On the next line, at the prompt β or ρ, highlight ≠ 0 and press ENTER. 5. Leave the line for RegEQ: blank. 6. Highlight Calculate and press ENTER. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 12 |... |
. Check it on your screen. 2. Go to LinRegTTest and enter the lists. 3. At RegEq, press VARS and arrow over to Y-VARS. Press 1 for 1:Function. Press 1 for 1:Y1. Then, arrow down to Calculate and do the calculation for the line of best fit. 4. Press Y= (you will see the regression equation). 5. Press GRAPH, and the line... |
of the x-coordinates times the y-coordinates, minus the quantity of the sum of the x-coordinates times the sum of the y-coordinates, all divided by the square root of the quantity of data points times the sum of the x-coordinates squared minus the square of the sum of the x-coordinates, times the number of data points... |
. • The line of best fit is: ŷ = –173.51 + 4.83x. • The correlation coefficient is r =.6631. • The coefficient of determination is r2 =.66312 =.4397. Interpret r2 in the context of this example. • Approximately 44 percent of the variation (0.4397 is approximately 0.44) in the final exam grades can be explained by the v... |
relationship between x and y in the population. If the test concludes the correlation coefficient is not significantly different from zero (it is close to zero), we say the correlation coefficient is not significant. • Conclusion: There is insufficient evidence to conclude there is a significant linear relationship be... |
: 1. Complete the same steps as the LinRegTTest performed previously in this chapter, making sure on the line prompt for β or σ, ≠ 0 is highlighted. 2. When looking at the output screen, the p-value is on the line that reads p =. If the p-value is less than the significance level (α = 0.05): • Decision: Reject the null... |
different from zero. Because r is significant and the scatter plot shows a linear trend, the regression line can be used to predict final exam scores. METHOD 2: Using a Table of Critical Values to Make a Decision The 95 Percent Critical Values of the Sample Correlation Coefficient Table (Table 12.9) can be used to giv... |
of best fit, you compute that r = 0.5204 using n = 9 data points, and the critical values are ±0.666. Can the line be used for prediction? Why or why not? Example 12.8 Suppose you computed r = 0.776 and n = 6, with df = 6 -– 2 = 4. The critical values are – 0.811 and 0.811. Since 0.776 is between the two critical valu... |
of best fit associated with each correlation coefficient can be used to predict a y value. If it helps, draw a number line. a. r = –0.567 and the sample size, n, is 19. To solve this problem, first find the degrees of freedom. df = n - 2 = 17. Then, using the table, the critical values are ±0.456. –0.567 < –0.456, or ... |
this. The assumptions underlying the test of significance are as follows: • There is a linear relationship in the population that models the sample data. Our regression line from the sample is our best estimate of this line in the population. • The y values for any particular x value are normally distributed about the... |
enter 90 into the equation for x and calculate a corresponding y value, the y value that you get will not be reliable. To understand how unreliable the prediction can be outside the x values observed in the data, make the substitution x = 90 into the equation: ŷ = –173.51 + 4.83⎛ ⎝90⎞ ⎠ = 261.19. This OpenStax book is... |
can determine if an outlier is, indeed, an influential point. The new regression will show how omitting the outlier will affect the correlation among the variables, as well as the fit of the line. A graph showing both regression lines helps determine how removing an outlier affects the fit of the model. Identifying Ou... |
we did with the equation of the regression line and the correlation coefficient, we will use technology to calculate this standard deviation for us. Using the LinRegTTest with these data, scroll down through the output screens to find s = 16.412. Line Y2 = –173.5 + 4.83x – 2(16.4), and line Y3 = –173.5 + 4.83x + 2(16.... |
. s is the standard deviation of all the y – ŷ = ε values, where n is the total number of data points. If each residual is calculated and squared, and the results are added, we get the SSE. The standard deviation of the residuals is calculated from the SSE as NOTE We divide by (n – 2) because the regression model invol... |
the outlier from L1 and L2. Using the LinRegTTest, found under Stat and Tests, the new line of best fit and correlation coefficient are the following: ŷ = − 355.19 + 7.39x and r = 0.9121. The slope is now 7.39, compared to the previous slope of 4.83. This seems significant, but we need to look at the change in r-value... |
+ 12 11εi 2 (Recall that yi – ŷi = εi). 2 = ⎠ = 2,440 = SSE. The result, SSE, is the sum of squared errors. Next, calculate s, the standard deviation of all the y – ŷ = ε-values where n = the total number of data points. The calculation is s = SSE n – 2. For the third exam/final exam example, s = 2440 11 – 2 = 16.47. ... |
to receive on the final exam? Is this the same as the prediction made using the original line? Solution 12.12 Using the new line of best fit, ŷ = –355.19 + 7.39(73) = 184.28. A student who scored 73 points on the third exam would expect to earn 184 points on the final exam. The original line predicted that ŷ = –173.51... |
equation of the line of best fit. c. See Figure 12.17. d. r = 0.8694. The number of data points is n = 14. Use the 95 Percent Critical Values of the Sample Correlation Coefficient table at the end of Chapter 12: In this case, df = 12. The corresponding critical values from the table are ±0.532. Since 0.8694 > 0.532, r... |
Use regression to find the line of best fit and the correlation coefficient. d. e. Interpret the significance of the correlation coefficient. Is there a linear relationship between the variables? 720 Chapter 12 | Linear Regression and Correlation f. Find the coefficient of determination and interpret it. g. What is th... |
19 Analyze the Data This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 12 | Linear Regression and Correlation 723 Enter your data into a calculator or computer. Write the linear equation, rounding to four decimal places. 1. Calculate the following: a. a = ______ b. b = ______ c. cor... |
answer for the following scenarios: a. For a textbook with 400 pages, predict the cost. b. For a textbook with 600 pages, predict the cost. 3. Obtain the graph on a calculator or computer. Sketch the regression line. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 12 | Linear Re... |
your scatter plot. Discussion Questions 1. Is the correlation significant? Explain how you determined this in complete sentences. 2. 3. Is the relationship a positive one or a negative one? Explain how you can tell and what this means in terms of weight and fuel efficiency. In one or two complete sentences, what is th... |
b is called a coefficient) is called the slope. The slope describes the rate of change between the independent and dependent variables; in other words, the rate of change describes the change that occurs in the dependent variable as the independent variable is changed. In the equation y = a + bx, the constant a is call... |
The conditions for regression are as follows: • Linear: In the population, there is a linear relationship that models the average value of y for different values of x. • Independent: The residuals are assumed to be independent. • Normal: The y values are distributed normally for any value of x. • Equal variance: The s... |
. FORMULA REVIEW 12.1 Linear Equations where a is the y-intercept and b is the slope. Standard Deviation of the Residuals: y = a + bx, where a is the y-intercept and b is the slope. The variable x is the independent variable and y is the dependent variable. s = SSE n − 2, where SSE = sum of squared errors, and n = the ... |
for free at http://cnx.org/content/col30309/1.8 Chapter 12 | Linear Regression and Correlation 731 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 48,634 59,660 78,530 78,834 71,874 68,505 59,347 47,149 38,393 25,174 25,522 25,643 26,464 31,335 36,560 41,055 44,730 49,095 49,456 38,510 20,736 19,005 1... |
Table 12.14 50 72 45 51 80 96 65 90 Fill in the following chart as a first step in finding the line of best fit, using the median–median approach. Group x (no. of hours spent studying) y (final exam grades) Median x Value Median y Value 1 2 3 Table 12.15 Use the following information to answer the next five exercises.... |
the properties is 1,345 acres. The rate at which one person can mow is ŷ = 1350 – 1.2x, where x is the number of hours and ŷ represents the number of acres left to mow. 31. How many acres are left to mow after 20 hours of work? 32. How many acres are left to mow after 100 hours of work? 33. How many hours does it take... |
time (years) and the number of diagnosed flu cases reported in the United States? 39. Plot the two points on the graph. Then, connect the two points to form the regression line. 40. Write the equation: ŷ = ____________. 41. Hand-draw a smooth curve on the graph that shows the flow of the data. 42. Does the line seem t... |
variable and the dependent variable. a. A study is done to determine whether elderly drivers are involved in more motor vehicle fatalities than other drivers. The number of fatalities per 100,000 drivers is compared with the age of drivers. Insurance companies base life insurance premiums partially on the age of the a... |
–24 25–34 35–54 55–74 75+ Table 12.20 38 36 24 20 18 28 a. For each age group, pick the midpoint of the interval for the x value. For the 75+ group, use 80. b. Using age as the independent variable and number of driver deaths per 100,000 people as the dependent variable, make a scatter plot of the data. c. Calculate th... |
the Fine Dining section, 10th edition, for various pages is given in Table 12.22. Page Number Maximum Value ($) 4 14 25 32 43 57 72 85 90 Table 12.22 16 19 15 17 19 15 16 15 17 a. Decide which variable should be the independent variable and which should be the dependent variable. b. Draw a scatter plot of the ordered ... |
for the next Summer Olympics. Do you think your answer is reasonable? Why or why not? 740 65. State Alabama Colorado Hawaii Iowa Maryland Missouri 7 8 6 4 8 8 New Jersey 9 Ohio South Carolina Utah Wisconsin Table 12.24 4 13 4 9 Chapter 12 | Linear Regression and Correlation No. of Letters in Name Year Entered the Unio... |
Chapter 12 | Linear Regression and Correlation 67. In Table 12.31, the height (sidewalk to roof) of notable tall buildings in America is compared with the number of stories of the building (beginning at street level). Height (in feet) Stories 1,050 428 362 529 790 401 380 1,454 1,127 700 Table 12.26 57 28 26 40 60 22 ... |
point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain. f. An ecologist wants to predict how many birds will join another colony of sparrow hawks to which 70 percent of the adults from the previous year have returned. What is the prediction? ... |
. How well does the regression line fit the data? Explain your response. e. Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain. 744 Chapter 12 | Linear Regression and Correlation 71. A researcher is investigating whether population i... |
n.d.). Retrieved from https://www.cdc.gov/ National Center for HIV/AIDS, Viral Hepatitis, STD, and TB Prevention. (n.d.). Centers for Disease Control and Prevention. Retrieved from https://www.cdc.gov/nchhstp/default.htm 12.4 Prediction (Optional) Centers for Disease Control and Prevention. (n.d.). Retrieved from https... |
and find the estimated number of family members attending college. f. Based on the data in Table 12.31, is there a linear relationship between the year and the average number of family members attending college? g. Using the least-squares line, estimate the number of family members attending college for 1960 and 1995.... |
in Table 12.33. Size (ounces) Cost ($) Cost per Ounce 16 32 64 200 Table 12.33 3.99 4.99 5.99 10.99 748 75. 76. Chapter 12 | Linear Regression and Correlation a. Using size as the independent variable and cost as the dependent variable, draw a scatter plot. b. Does it appear from inspection that there is a relationshi... |
udential Insurance Company, the costs of approximate probate fees and taxes for selected net taxable estates are as follows: Net Taxable Estate ($) Approximate Probate Fees and Taxes ($) 600,000 750,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 Table 12.34 30,000 92,500 203,000 438,000 688,000 1,037,000 1,350,0... |
the data? Why or why not? h. Are there any outliers in the data? i. What is the slope of the least-squares (best-fit) line? Interpret the slope. 79. Table 12.36 shows the average heights for American boys in 1990. Age (years) Height (centimeters) Birth 2 3 5 7 10 14 Table 12.36 50.8 83.8 91.4 106.6 119.3 137.1 157.5 a... |
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