question 1

Below are four bivariate data sets and their scatter plots. (Note that all of the scatter plots are displayed with the same scale.) Each data set is made up of sample values drawn from a population. 1.0 3.6 1.0 7.6 2.0 5.9 2.0 6.9 3.0 70 3.0 7.8 4.0 4.4 4.0 6.1 5.0 5.2 5.0 7.1 6.0 76 6.0 4.6 7.0 5.2 7.0 4.6 8.0 70 8.0 3.2 9.0 8.7 9.0 4.3 10.0 7 5 Figure 1 10 0 3.4 Figure 2 IT 1.0 1.0 10 79 2.0 20 52 3.0 3.0 3.0 10.2 4.0 4.0 4.0 59 5.0 5.0 50 20 5.0 6.0 6.0 46 7.0 7.0 70 88 8.0 8.0 80 36 9.0 9.0 90 9.1 10.0 10.0 Figure 3 10.0 72 Figure 4 Answer the following questions about the relationships between pairs of variables and the values of r, the sample correlation coefficient. The same response may be the correct answer for more than one question.(a) Which data set indicates the strongest positive linear relationship between its two variables? (Choose one) the u, v data set the x, y data set the w, t data set the m, n data set(b) Which data set has an apparent negative, but not perfect, linear relationship between its two variables? (Choose one) the u, v data set the x, y data set the w, t data set the m, n data set(c) For which data set is the sample correlation coefficient r equal to - 17 (Choose one) the w, t data set the x, y data set the u, v data set none of the data sets the m, n data set(d) For which data set is the sample correlation coefficient r closest to 0? (Choose one) the u, v data set the x, y data set the w, t data set the m, n data setBelow are four bivariate data sets and their scatter plots. (Note that all of the scatter plots are displayed with the same scale.) Each data set is made up of sample values drawn from a population. F 11- 10 3.2 10 8.2 2.0 3.8 20 3.0 3.0 3.5 30 9.9 40 5.0 40 63 5- 50 4.4 50 21 6.0 7.2 6.0 4.6 70 6.5 7.0 8.6 80 7.5 80 3.8 90 7.0 90 9.7 10.0 8.1 Figure 1 10.0 6.5 Figure 2 10 7.7 1.0 7.3 20 7.1 2.0 8.9 30 81 3.0 6.5 4.0 6.2 4.0 5.7 5 0 73 5.0 8.0 60 45 6.0 5.0 70 4.6 7.0 4.7 80 3.4 8.0 6.6 90 42 9.0 5.5 10.0 3.0 Figure 3 10.0 4.4 Figure 4 Answer the following questions about the relationships between pairs of variables and the values of r, the sample correlation coefficient. The same response may be the correct answer for more than one question.(a) For which data set is the sample correlation coefficient / closest to - 1? (Choose one) the x, y data set the u, v data set the w, t data set the m, n data set (b) For which data set is the sample correlation coefficient r equal to 1? (Choose one) the x, y data set the u, v data set the w, t data set the m, n data set(c) For which data set is the sample correlation coefficient + closest to 0? (Choose one) the x, y data set the u, v data set the w, t data set the m, n data set (d) Which data set indicates the strongest positive linear relationship between its two variables? (Choose one) the x, y data set the u, v data set the w, t data set the m, n data setThe well-known psychologist Dr. Elbod has established what he calls his Generalized Anxiety Scale (GAS). The GAS, which is a scale from 0 to 10, measures the "general anxiety" of an individual, with higher GAS scores corresponding to more anxiety. (Dr. Elbod's assessment of anxiety is based on a variety of measurements, both physiological and psychological.) The bivariate data below give the GAS score (denoted by x) and the number of hours of sleep last night (denoted by )) for each of the fifteen adults in a study. The least-squares regression line for these data has equation y = 8.29-0.26x. This line, along with a scatter plot of the sample data, is shown below. GAS score, x Sleep time, y (in hours) 1.5 8.9 6.6 5.8 9.0 5.8 3.7 8.2 $.1 5.5 5.8 7.7 3.6 7.8 Sleep time (in hours) 5.0 5.9 60 6.4 9.1 6.4 8.0 7.0 2.9 7.2 10 2.0 7.9 GAS score 1.1 7.1 4.1 6.6 Send data to calculator v Based on the study's data and the regression line, complete the following.(a) For these data, GAS scores that are greater than the mean of the GAS scores tend to be paired with sleep times that are (Choose one) the mean of the sleep times. greater than less than (b) According to the regression equation, for an increase of one in GAS score, there is a corresponding decrease of how many hours in sleep time?Can movie rental revenue be predicted? A movie studio wishes to determine the relationship between the revenue from rental of comedies on streaming services and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years, These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from streaming service rentals (in millions of dollars) for each of the fifteen movies. Also shown are the scatter plot and the least-squares regression line for the data. The equation for this line is y = 3.16+0.15x. Theater revenue, * Rental revenue, y (in millions of dollars) (in millions of dollars) 31.7 5.4 7.5 3.3 36.4 11.9 18- 61.8 10.9 44.7 7.3 27.5 11.5 49.0 16.5 (in millions of dollars) Rental revenue 28.0 20 66.7 9.0 25.7 7.2 14.6 1.8 10 70 13.7 9.2 25.3 Theater revenue 8.9 (in millions of dollars) 20.5 4.8 61.6 16.5 Send data to calculator v Based on the studio's data and the regression line, complete the following. -(a) For these data, values for theater revenue that are less than the mean of the values for theater revenue tend to be paired with values for rental revenue that are (Choose one) |the mean of the values for rental revenue. greater than V less than (b) According to the regression equation, for an increase of one million dollars in theater revenue, there is a corresponding increase of how many million dollars in rental revenue?An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (denoted by x, in millions of dollars) and the resulting percentage increase in sales (denoted by y) following the campaign, were presented by the firm. A scatter plot of the data is shown in Figure 1. Also given is the product of the campaign cost and the percentage increase in sales for each of the twelve campaigns. (These products, written in the column labelled "xy", may ald in calculations.) Campaign Increase in cost, X (in millions of sales, y xy dollars) (percent) 1.56 6.29 9.8124 3.96 7.01 27.7596 3.31 6.55 21.6805 3.00 6.59 19.77 Increase in sales (percent) 2.14 6.41 13.7174 3.50 6.83 23.905 2.20 6.75 14.85 1.33 6.39 B.4987 15 3.04 6.92 21.0369 Campaign cost 3.67 6.78 24 0826 (in millions of dollars) 1.65 6.60 10.89 Figure 1 2.29 6.56 15.0224 Send data to calculator What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formit as.) XThe well-known psychologist Dir. Elbod has established what he calls his Generalized Anxiety Scale (GAS). The GAS, which is a scale from 0 to 10, measures the "general anxiety" of an individual, with higher GAS scores corresponding to more anxiety. (Dr. Elbod's assessment of anxiety is based on a variety of measurements, both physiological and psychological.) We're interested in making predictions about individuals' sleep behavior based on their GAS scores. The bivariate data below give the GAS score (denoted by x] and the number of hours of sleep last night (denoted by )) for each of the fifteen adults participating in a study. A scatter plot of the data is shown in Figure 1. Also given is the product of the GAS score and the sleep time for each of the fifteen adults. (These products, written in the column labelled "xy", may aid in calculations.) GAS score, x Sleep time, y (in hours) 8.5 5.6 49.84 6.5 5.7 37.05 3.7 8.3 30.71 9.1 56.42 5.1 6.0 30.6 1.1 7.7 8.47 Sleep time 8.0 5.5 44 (in hours) 3.0 20 7 6.1 4.2 50.02 1.9 8.1 15.35 6.2 7.0 57.4 1.4 B.8 12.32 GAS score 3.4 7.7 26.18 Figure 1 7.1 6.5 46-15 3.9 7.3 28.47 Send data to calculator What is the sample correlation coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places. (If necessary, consult a list of formulas. ) X ?A laboratory in Florida is interested in finding the mean chloride level for a healthy resident in the state. A random sample of 80 healthy residents has a mean chloride level of 99 TI]. If it is known that the chloride levels in healthy individuals residing in Florida have a standard deviation of 42 , find a 95% confidence interval for the true mean chloride level of all healthy Florida residents. Then give its lower limit and upper limit. Camir your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: III Upper limit: I] The breaking strengths of cables produced by a certain manufacturer have a standard deviation of 86 pounds. A random sample of 70 newly manufactured cables has a mean breaking strength of 1700 pounds. Based on this sample, nd a 99% confidence interval for the true mean breaking strength of all cables produced by this manufacturer: Then give its lower limit and upper limit. Cam.r your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: I x 33 O Upper limit: Suppose that a researcher is interested in estimating the mean systolic blood pressure, p, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate p" Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 26 mm Hg, what is the minimum sample size needed for the researcher to be 99% confident that his estimate is within 4 mm Hg of u? Cam.r your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) A psychologist is studying the self image of smokers, which she measures by the selfimage (SI) score from a personality inventory. She would like to estimate the mean SI score, u, for the population of all smokers. She plans to take a random sample of 51 scores for smokers and estimate u via this sample. Assuming that the standard deviation of 51 scores for the population of all smokers is 82, what is the minimum sample size needed for the psychologist to be 90% confident that her estimate is within 15 of u? Cany your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) D xo