804 APPENDIX D 5. There is not sufficient evidence to warrant rejection of the null hypothesis that the digits are all equally likely. Although we cannot conclude that the sample data support the claim that the digits are equally likely (because we can’t support a null hypothesis), it does appear that Statdisk generates the digits so that they are equally likely. 6. H0: Surviving the sinking is independent of whether the person is a man, woman, boy, or girl. H1: Surviving the sinking and whether the person is a man, woman, boy, or girl are somehow related. 7. Chi-square distribution. 8. Right-tailed. 9. df = 3 10. There is sufficient evidence to warrant rejection of the claim that surviving the sinking is independent of whether the person is a man, woman, boy, or girl. Most of the women survived, 45% of the boys survived, and most girls survived, but only about 20% of the men survived, so it appears that the rule was followed quite well. Chapter 11: Review Exercises 1. Test statistic: x2 = 186.332. P@value = 0.000 (Table: 60.005). Critical value: x2 = 24.725. There is sufficient evidence to warrant rejection of the claim that weather-related deaths occur in the different months with the same frequency. The warmer months appear to have disproportionately more weather-related deaths, and that is likely due to the fact that vacations and outdoor activities are much greater during those months. 2. Test statistic: x2 = 396.014. Critical value: x2 = 15.507 (assuming a 0.05 significance level). P-value: 0.000 (Table: 60.005). There is sufficient evidence to warrant rejection of the claim that the observed frequencies fit the distribution from Benford’s law. It appears that the data are from matches in which cheating may have occurred. 3. Test statistic: x2 = 9.750. P@value = 0.002 (Table: 60.005). Critical value: x2 = 6.635. There is sufficient evidence to warrant rejection of the claim that success is independent of the type of treatment. The results suggest that the surgery treatment is better. 4. Test statistic: x2 = 58.393. Critical value: x2 = 7.815. P-value: 0.000 (Table: 60.005). There is sufficient evidence to warrant rejection of the claim that success is independent of the treatment. Although these results of this test do not tell us which treatment is best, we can see from the table that the success rates of 81.8%, 44.6%, 95.9%, and 77.3% suggest that the best treatment is to use a non-weight-bearing cast for 6 weeks. These results suggest that the increasing use of surgery is a treatment strategy that is not supported by the evidence. Chapter 11: Cumulative Review Exercises 1. a. Here are two different key questions that are appropriate for the data: (1) Is there a correlation between the scores of the females and the scores of their brothers? (2) For the paired scores, is there a significant difference between the scores of the siblings? b. (1) Use the linear correlation coefficient, as in Section 10-1. (2) Use the methods for inferences about differences from matched pairs, as in Section 9-3. 5. Test statistic: x2 = 25.571. P-value = 0.000 (Table: 60.005). Critical value: x2 = 3.841. There is sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication. The results suggest that polygraphs are effective in distinguishing between truths and lies, but there are many false positives and false negatives, so they are not highly reliable. 7. Test statistic: x2 = 576.224. P-value = 0.000 (Table: 60.005). Critical value: x2 = 3.841. There is sufficient evidence to warrant rejection of the claim of independence between texting while driving and driving when drinking alcohol. Those two risky behaviors appear to be somehow related. 9. Test statistic: x2 = 12.162. P-value = 0.001 (Table: 60.005). Critical value: x2 = 3.841. There is sufficient evidence to warrant rejection of the claim that whether students purchased gum or kept the money is independent of whether they were given four quarters or a $1 bill. It appears that there is a denomination effect. 11. Test statistic: x2 = 6.343. P@value = 0.012 (Table: 60.05). Critical value: x2 = 3.841. There is sufficient evidence to warrant rejection of the claim of independence between gender and success in challenging referee calls. However, with success rates of 29.1% for men and 26.7% for women, the difference does not appear to have practical significance. 13. Test statistic: x2 = 16.091. P@value = 0.001 (Table: 60.005). Critical value: x2 = 11.345. There is sufficient evidence to warrant rejection of the claim of independence between gender and eye color. However, because the sample data were reported, it is possible that the sample is not representative of the population. 15. Test statistic: x2 = 2.925. P-value = 0.232 (Table: 70.10). Critical value: x2 = 5.991. There is not sufficient evidence to warrant rejection of the claim that getting a cold is independent of the treatment group. The results suggest that echinacea is not effective for preventing colds. 17. Test statistic: x2 = 20.271. P-value = 0.0011 (Table: 60.005). Critical value: x2 = 15.086. There is sufficient evidence to warrant rejection of the claim that cooperation of the subject is independent of the age category. The age group of 60 and over appears to be particularly uncooperative. 19. Test statistic: x2 = 50.446. P-value = 0.000 (Table: 60.005). Critical value: x2 = 5.991. There is sufficient evidence to warrant rejection of the claim of independence between the state and whether a car has front and rear license plates. It does not appear that the license plate laws are followed at the same rates in the three states. 21. Unrounded test statistics: x2 = 3.197517514 and z = 1.788160371 so that x2 = z2. Critical values: x2 = 3.841 and z = {1.96 (or {1.959963986 from technology), so x2 = z2. Chapter 11: Quick Quiz 1. H0: p0 = p1 = g = p9. H1: At least one of the probabilities is different from the others. 2. O = 45 and E = 50. 3. Right-tailed. 4. df = 9
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