798 APPENDIX D 10. a. Key question: Is there a correlation between the numbers of pleasure boats and the numbers of manatee fatalities? b. A scatterplot (see Section 2-2) would be helpful in visualizing whether there is a correlation. (The following chapter will introduce much more thorough and objective criteria for analyzing correlations.) c. A scatterplot reveals that there does not appear to be a correlation between the numbers of pleasure boats and the numbers of manatee deaths. Chapter 10 Answers Section 10-1 1. a. r is a statistic that represents the value of the linear correlation coefficient computed from the paired sample data, and r is a parameter that represents the value of the linear correlation coefficient that would be computed by using all of the paired data in the population of all statistics students. b. The value of r is estimated to be 0, because it is likely that there is no correlation between heights of statistics students and their scores on the first statistics test. c. The value of r does not change if the heights are converted from centimeters to inches. 3. No. A correlation between two variables indicates that they are somehow associated, but that association does not necessarily imply that one of the variables has a direct effect on the other variable. Correlation does not imply causality. 5. Yes. r = 0.963. P-value = 0.000. Critical values: {0.268 (Table: {0.279 approximately). There is sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes. It is easier to measure the chest size of a bear than the weight, which would require lifting the bear onto a scale. It does appear that chest size could be used to predict weight. c. It appears that eyewitness memory of police is better with a non-stressful interrogation than with a stressful interrogation. H0: m1 = m2 and H1: m1 7 m2. Test statistic: t = 2.843. P@value = 0.0029 (Table: P@value 6 0.005). Critical value: t = 1.665 (Table: 1.685). 90% CI: 3.27 6 m1 - m2 6 12.53 (Table: 3.22 6 m1 - m2 6 12.58). Reject H0. There is sufficient evidence to support the claim that eyewitness memory of police is better with a non-stressful interrogation than with a stressful interrogation. 7. a. Key question: How do the different categories compare in terms of the numbers of deaths? b. Construct an effective graph such as a Pareto chart so that we can see which causes of death are most significant. c. A Pareto chart or bar chart or pie chart shows that pollution is the largest cause of deaths, followed by tobacco use. Deaths from the other causes are relatively much lower. 8. a. Key question: Is the mean height of supermodels greater than (or different from) 162 cm, so that supermodels are generally taller than (or have heights different from) adult women in the general population? b. Use a hypothesis test or confidence interval for an inference involving a single population mean (as in Section 8-3). c. The data support the claim that supermodels are taller than (or have heights different from) the mean of 162 cm for adult women in the general population. H0: m = 162 cm. H1: m 7 162 cm. Test statistic: t = 33.082. P@value = 0.0000 (Table: 6 0.005). Critical value: t = 1.753 (assuming a 0.05 significance level). 90% confidence interval: 176.4 cm 6 m 6 178.1 cm. Reject H0. (If testing H1: m ≠ 162 cm, the test statistic and P-value will be the same.) There is sufficient evidence to support the claim that supermodels have heights with a mean that is greater than the mean height of 162 cm for women in the general population. Supermodels appear to be taller than typical women. 9. a. Key question: Are the numbers selected in a way that appears to be random, with roughly the same frequency for each number? b. Construct a histogram or dotplot to visualize the frequencies. c. The graph shows that the numbers do appear to be drawn with roughly the same frequency. (Chapter 11 will introduce a procedure for testing “goodness-of-fit” with a uniform distribution, and that procedure is much more thorough and objective.)
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