APPENDIX D 807 Chapter 13 Answers Section 13-2 1. a. The only requirement for the matched pairs is that they constitute a simple random sample. b. There is no requirement of a normal distribution or any other specific distribution. c. The sign test is “distribution-free” in the sense that it does not require a normal distribution or any other specific distribution. 3. H0: There is no difference between hospital admissions due to traffic accidents that occur on Friday the 6th and those that occur on the following Friday the 13th. H1: There is a difference between hospital admissions due to traffic accidents that occur on Friday the 6th and those that occur on the following Friday the 13th. The sample data do not contradict H1 because the numbers of positive signs (1) and negative signs (5) are not exactly the same. 5. The test statistic of x = 3 is not less than or equal to the critical value of 1 (from Table A-7). There is not sufficient evidence to warrant rejection of the claim of no difference. Based on the given data, there does not appear to be a significant difference between measured weights and reported weights. 7. The test statistic of z = -1.47 results in a P-value of 0.1416, and it does not fall in the critical region bounded by z = -1.96 and 1.96. There is not sufficient evidence to warrant rejection of the claim that there is no significant difference between the numbers of words spoken by males and females in couple relationships. Based on the given data, there does not appear to be a significant difference. 9. The test statistic of z = -1.30 results in a P-value of 0.1936, and it is not in the critical region bounded by z = -1.96 and 1.96. There is not sufficient evidence to warrant rejection of the claim that toast will land with the buttered side down 50% of the time. 11. The test statistic of z = -2.00 results in a P-value of 0.0455, and it is in the critical region bounded by z = -1.96 and 1.96. There is sufficient evidence to warrant rejection of the claim that the coin toss is fair in the sense that neither team has an advantage by winning it. The coin toss does not appear to be fair. 13. The test statistic of z = -4.91 results in a P-value of 0.0000, and it is in the critical region bounded by z = -2.575 and 2.575. There is sufficient evidence to warrant rejection of the claim that the median is equal to 98.6°F. 15. The test statistic of z = -29.67 results in a P-value of 0.0000, and it is in the critical region bounded by z = -2.575 and 2.575. There is sufficient evidence to warrant rejection of the claim that smokers have a median cotinine level equal to 2.84 ng>mL. 17. Second approach: The test statistic of z = -4.29 results in a P-value of 0.0000, and it is in the critical region bounded by z = -1.645, so the conclusions are the same as in Example 4. Third approach: The test statistic of z = -2.82 results in a P-value of 0.0024, and it is in the critical region bounded by z = -1.645, so the conclusions are the same as in Example 4. The different approaches can lead to very different results; see the test statistics of -4.21, -4.29, and -2.82. The conclusions are the same in this case, but they could be different in other cases. Chapter 12: Cumulative Review Exercises 1. a. 15.9 years, 13.1 years, 22.7 years b. 9.9 years, 9.0 years, 18.6 years c. 97.4 years2, 80.3 years2, 346.1 years2 d. Visual inspection of the data shows that among the monarchs, the values of 59 years and 63 years appear to be possible outliers, but they are not outliers according to the criterion of being above the third quartile Q3 by more than 1.5 times the interquartile range. e. Ratio level of measurement 2. Test statistic: t = 1.136. P@value = 0.2610 (Table: 70.20). Critical values assuming a 0.05 significance level: t = {2.006 (Table: {2.069). Fail to reject H0: m1 = m2. There is not sufficient evidence to support the claim that there is a difference between the mean longevity times of presidents and popes. 3. Because the pattern of the points is reasonably close to a straightline pattern, the longevity times of presidents do appear to be from a population with a normal distribution. 4. 12.7 years 6 m 6 19.1 years. We have 95% confidence that the limits of 12.7 years and 19.1 years contain the value of the population mean for longevity times of presidents. 5. a. H0: m1 = m2 = m3 b. Because the P-value of 0.054 is greater than the significance level of 0.05, fail to reject the null hypothesis of equal means. There is not sufficient evidence to warrant rejection of the claim that the three means are equal. The three populations do not appear to have means that are significantly different. 6. a. 0.5563 (Table: 0.5552) b. 0.3434 (Table: 0.3446) c. 1>256 or 0.00391 d. 5.591 g 7. Test statistic: x2 = 85.945. P-value: 0.000 (Table: 60.005). Critical value: x2 = 3.841. Reject the null hypothesis of independence between physical activity within 7 days after an acute concussion and symptoms 28 days after the concussion. It appears that early physical activity during the week after a concussion does have an effect on symptoms 28 days after a concussion. 8. a. Because the vertical scale begins at 15 instead of 0, the graph is deceptive by exaggerating the differences among the frequencies. b. No. A normal distribution is approximately bell-shaped, but the given histogram is far from being bell-shaped. Because the digits are supposed to be equally likely, the histogram should be flat with all bars having approximately the same height. c. The frequencies are 19, 21, 22, 21, 18, 23, 16, 16, 22, 22. Test statistic: x2 = 3.000. P@value = 0.964 (Table: 70.95). Critical value: x2 = 16.919 (assuming a 0.05 significance level). There is not sufficient evidence to warrant rejection of the claim that the digits are selected from a population in which the digits are all equally likely. There does not appear to be a problem with the lottery.
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