802 APPENDIX D 3. a. For professional horse jockeys, is there a correlation between weight and number of top three race finishes? b. Use the methods of Section 10-1 to test for a linear correlation. c. r = -0.060. P@value = 0.869 (Table: 7 0.05). Critical values (assuming a 0.05 significance level): r = {0.632. There is not sufficient evidence to support the claim that there is a linear correlation between weight and the number of top three race finishes. 4. a. Because the table lists time series data, a key question is this: What is the trend of the data over time? b. Use the methods of Section 2-3 to construct a time series graph that would reveal a trend of the data over time. c. A time series graph clearly shows that there is a distinct trend of steadily increasing numbers of digital buyers over time. Businesses should ensure they can market and sell their goods and services online. 5. a. What is an estimate of the proportion of all adults who have wireless earbuds? b. Use the methods of Section 7-1 to construct a confidence interval estimate of the proportion of all adults who use wireless earbuds. c. 95% confidence interval estimate of p: 0.280 6 p 6 0.320. With 95% confidence, it is estimated that between 28.0% and 32.0% of all adults have wireless earbuds. (It would also be reasonable to conduct a hypothesis test, such as a test of the claim that fewer than 50% of adults have wireless earbuds. For that test, the test statistic is z = -17.95 and the P-value is 0.0000 so there is sufficient evidence to support the claim that fewer than 50% of adults have wireless earbuds.) 6. a. Is Stephen Curry significantly tall in the population of adult males? b. Using the methods of Section 3-3, convert Stephen Curry’s height to a z score and use the range rule of thumb to determine whether his height is significantly high. c. Converting Stephen Curry’s height to a z score, we get z = 1x - m2>s = 1191 - 174.122>7.10 = 2.38. Stephen Curry’s height is 2.38 standard deviations above the mean, so his height is significantly high. 7. a. Is the mean amount provided by the new device equal to 16 ounces? Is there anything else about the data suggesting that there is a problem with the new device? b. Explore the sample data to see if there are any undesirable characteristics. Use the methods of Section 8-3 to test the claim that the mean of the amounts is equal to 16 ounces. c. Although there is no linear correlation between time and height, the scatterplot shows a very distinct pattern revealing that time and height are associated by some function that is not linear. (The scatterplot appears to depict a parabola. The quadratic regression equation is y = -4.44x2 + 9.13x + 0.0482.) 4. a. NICOTINE = -0.443 + 0.0968 TAR - 0.0262 CO, or yn = -0.443 + 0.0968x 1 -0.0262x2. b. R2 = 0.936; adjusted R2 = 0.910; P-value = 0.001. c. With high values of R2 and adjusted R2 and a small P-value of 0.001, it appears that the regression equation can be used to predict the amount of nicotine given the amounts of tar and carbon monoxide. d. The predicted value is 1.39 mg or 1.4 mg rounded, which is close to the actual value of 1.3 mg of nicotine. Chapter 10: Cumulative Review Exercises 1. a. Is there a difference between the mean IQ score of airline passengers and the mean IQ score of police officers? b. Test for a difference between the means of two independent populations using the methods of Section 9-2. c. H0: m1 = m2. H1: m1 ≠ m2. Test statistic: t = -1.557. P@value = 0.1516 (Table: P@value 7 0.05). Critical values (assuming a 0.05 significance level): t = {2.239 (Table: {2.262). Fail to reject H0. There is not sufficient evidence to support the claim that there is a difference between the mean IQ score of airline passengers and the mean IQ of police officers. (This 95% confidence interval could also be used: -20.0 6 m1 - m2 6 3.59. Because the confidence interval includes 0, there is not sufficient evidence to support the claim that there is a difference between the mean IQ score of airline passengers and the mean IQ of police officers.) 2. a. Was the training course effective in raising the IQ scores? That is, do the “before - after” differences have a mean that is less than 0, showing that the course is effective in raising IQ scores? b. Use the methods of Section 9-3 to test the claim that the mean of the “before - after” differences is less than 0, showing that the course is effective with larger “after” scores. c. H0: md = 0. H1: md 6 0. Test statistic: t = -1.541. P@value = 0.0789 (Table: P@value 7 0.05). Critical value (assuming a 0.05 significance level): t = -1.833. Fail to reject H0. There is not sufficient evidence to support the claim that the course is effective with higher “after” scores. (This 90% confidence interval could also be used: -18.0 6 md 6 1.56). Because the confidence interval includes 0, there is not sufficient evidence to support the claim that the course is effective with higher “after” scores.
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