APPENDIX D 791 6. H0: p = 0.5. H1: p 7 0.5. Test statistic: z = 10.18. P-value = 0.0000 (Table: 0.0001). Critical value: z = 2.33. Reject H0. There is sufficient evidence to support the claim that the proportion of male deaths is greater than 1>2. More males are involved in certain outdoor activities such as construction, fishing, and golf. 7. 0.745 6 p 6 0.836. Because the entire confidence interval is greater than 0.5, it does not seem feasible that males and females have equal chances of being killed by lightning. The confidence interval indicates that the proportion of male lightning deaths is substantially greater than 0.5. 8. a. 0.512 b. 0.008 c. 0.992 d. 0.205 e. m = 40.0 males; s = 2.8 males f. Yes. Using the range rule of thumb, significantly high values are m + 2s or greater. With m + 2s = 45.6, values above 45.6 are significantly high, so 46 would be a significantly high number of male victims in a group of 50. Using probabilities, P(46 or more male victims among 50) = 0.0185, which is very small, suggesting that 46 is significantly high. Chapter 9 Answers Section 9-1 1. The samples are simple random samples that are independent. For each of the two groups, the number of successes is at least 5 and the number of failures is at least 5. (Depending on what we call a success, the four numbers are 33, 115, 201,196, and 200,630 and all of those numbers are at least 5.) The requirements are satisfied. 3. a. H0: p1 = p2. H1: p1 6 p2. b. There is sufficient evidence to support the claim that the rate of polio is less for children given the Salk vaccine than for children given a placebo. The Salk vaccine appears to be effective. 5. H0: p1 = p2. H1: p1 7 p2. Test statistic: z = 12.82. P-value: 0.0000. Critical value: z = 2.33. Reject H0. There is sufficient evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves. 7. a. H0: p1 = p2. H1: p1 ≠ p2. Test statistic: z = -0.62. P-value: 0.5359 (Table: 0.5352). Critical values: z = {1.96. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that when dropped, buttered toast and toast marked with an X have the same proportion that land with the buttered>X side down. b. 95% CI: -0.260 6 p1 - p2 6 0.135. Because the confidence interval limits do contain 0, there is a not a significant difference between the two sample proportions. There is not sufficient evidence to warrant rejection of the claim that when dropped, buttered toast and toast marked with an X have the same proportion that land with the buttered>X side down. 9. a. H0: p1 = p2. H1: p1 6 p2. Test statistic: z = -7.94. P-value: 0.0000 (Table: 0.0001). Critical value: z = -2.33. Reject H0. There is sufficient evidence to support the claim that the rate of right-handedness for those who prefer to use their left ear for cell phones is less than the rate of right-handedness for those who prefer to use their right ear for cell phones. individual values, so the result does not suggest that each of the 40 males has a red blood cell count below 5.4 million cells per microliter. 4. H0: p = 0.43. H1: p ≠ 0.43. Test statistic: z = 3.70. P-value: 0.0002. Critical values: z = {1.96. Reject H0. There is sufficient evidence to warrant rejection of the claim that the percentage who believe that they voted for the winning candidate is equal to 43%. There appears to be a substantial discrepancy between how people said that they voted and how they actually did vote. 5. a. A type I error is the mistake of rejecting a null hypothesis when it is actually true. A type II error is the mistake of failing to reject a null hypothesis when in reality it is false. b. Type I error: In reality, the percentage who voted for the winning candidate is equal to 43%, but we conclude that the percentage is different from 43%. Type II error: In reality, the percentage who voted for the winning candidate is different from 43%, but we fail to support that claim that the percentage is different from 43%. 6. a. False b. True c. False d. False e. False Chapter 8: Cumulative Review Exercises 1. a. 34.8 deaths b. 33.0 deaths c. 10.7 deaths d. 114.7 deaths2 e. 35.0 deaths f. The pattern of the data over time is not revealed by the statistics. A time-series graph would be very helpful in understanding the pattern over time. The data appear to be trending downward. 2. a. Ratio b. Discrete c. Quantitative d. No. The data are from recent and consecutive years, so they are not randomly selected. 3. a. 27.9 deaths 6 m 6 41.6 deaths. b. We have 99% confidence that the limits of 27.9 deaths and 41.6 deaths contain the value of the population mean. c. No. The data appear to be trending downward. Instead of having a stable population, the population characteristics appear to be changing over time. 4. H0: m = 72.6 deaths. H1: m 6 72.6 deaths. Test statistic: t = -15.804. P@value = 0.0000 (Table: P@value 6 0.005). Critical value: t = -2.539. Reject H0: m = 72.6 deaths. There is sufficient evidence to support the claim that the mean number of annual lightning deaths is now less than the mean of 72.6 deaths from the 1980s. Possible factors: Shift in population from rural to urban areas; better lightning protection and grounding in electric and cable and phone lines; better medical treatment of people struck by lightning; fewer people use phones attached to cords; better weather predictions. 5. Because the vertical scale starts at 50 and not at 0, the difference between the number of males and the number of females is exaggerated, so the graph is deceptive by creating the false impression that males account for nearly all lightning strike deaths. A comparison of the numbers of deaths shows that the number of male deaths is roughly 4 times the number of female deaths, but the graph makes it appear that the number of male deaths is around 12 times the number of female deaths.
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