Cumulative Review 581 4. A school administrator claims that the standard deviations of reading test scores for eighth-grade students are the same in Illinois and Georgia. A random sample of 16 test scores from Illinois has a standard deviation of 33.1 points, and a random sample of 15 test scores from Georgia has a standard deviation of 31.8 points. At a = 0.10, can you reject the administrator’s claim? Assume the samples are independent and each population has a normal distribution. (Adapted from National Center for Education Statistics) 5. A researcher claims that how families pay for college is distributed as shown in the pie chart. You randomly select 900 families and record how each pays for college. The table shows the results, where f is the frequency of each response. At a = 0.05, test the researcher’s claim. (Adapted from Sallie Mae, Inc.) Scholarships and grants 25.4% Parent borrowing 8.4% Student borrowing 13.4% Relatives and friends 1.3% Student income and savings 7.7% Parent income and savings 43.8% Survey results Response f Parent income and savings 393 Scholarships and grants 222 Student borrowing 120 Student income and savings 85 Parent borrowing 66 Relatives and friends 14 6. Reviewing a Movie The contingency table shows how a random sample of adults rated a newly released movie and generation. At a = 0.05, can you conclude that the adults’ ratings are related to generation? Rating Generation Excellent Good Fair Poor Gen X (ages 41–56) 97 42 26 5 Millennial (ages 25–40) 101 33 25 11 7. The figure shows the metacarpal bones in the human hand. The table shows the first metacarpal bone lengths (in millimeters) and the heights (in centimeters) of 12 adults. The equation of the regression line is ny = 1.746x + 92.536. (Adapted from the American Journal of Physical Anthropology) Metacarpal bone length, x 45 51 39 41 47 48 Height, y 171 178 157 163 172 183 Metacarpal bone length, x 47 43 47 42 40 46 Height, y 173 175 173 169 160 172 (a) Find the coefficient of determination r2 and interpret the results. (b) Find the standard error of estimate se and interpret the results. (c) Construct a 95% prediction interval for the height of an adult whose first metacarpal bone length is 50 millimeters. Interpret the results. Metacarpal bones 1 2 3 4 5 FIGURE FOR EXERCISE 7
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