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Chapter 9: Q.11.46 (page 460)
A sample size that will ensure a margin of error of at most the one specified.
The required sample size is 6, 766
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In Exercises 5鈥�20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).)
BMI We know that the mean weight of men is greater than the mean weight of women, and the mean height of men is greater than the mean height of women. A person鈥檚 body mass index (BMI) is computed by dividing weight (kg) by the square of height (m). Given below are the BMI statistics for random samples of females and males taken from Data Set 1 鈥淏ody Data鈥� in Appendix B.
a. Use a 0.05 significance level to test the claim that females and males have the same mean BMI.
b. Construct the confidence interval that is appropriate for testing the claim in part (a).
c. Do females and males appear to have the same mean BMI?
Female BMI: n = 70, \(\bar x\) = 29.10, s = 7.39
Male BMI: n = 80, \(\bar x\) = 28.38, s = 5.37
Using Confidence Intervals
a. Assume that we want to use a 0.05 significance level to test the claim that p1 < p2. Which is better: A hypothesis test or a confidence interval?
b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; P-value method; critical value method?
c. If we want to use a 0.05 significance level to test the claim that p1 < p2, what confidence level should we use?
d. If we test the claim in part (c) using the sample data in Exercise 1, we get this confidence interval: -0.000508 < p1 - p2 < - 0.000309. What does this confidence interval suggest about the claim?
Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\))
Regular Coke and Diet Coke Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includesweights (lb) of the contents of cans of Diet Coke (n= 36,\(\overline x \)= 0.78479 lb, s= 0.00439 lb) and of the contents of cans of regular Coke (n= 36,\(\overline x \)= 0.81682 lb, s= 0.00751 lb).
a. Use a 0.05 significance level to test the claim that the contents of cans of Diet Coke have weights with a mean that is less than the mean for regular Coke.
b. Construct the confidence interval appropriate for the hypothesis test in part (a).
c. Can you explain why cans of Diet Coke would weigh less than cans of regular Coke?
Testing Claims About Proportions. In Exercises 7鈥�22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
Ground vs. Helicopter for Serious Injuries A study investigated rates of fatalities among patients with serious traumatic injuries. Among 61,909 patients transported by helicopter, 7813 died. Among 161,566 patients transported by ground services, 17,775 died (based on data from 鈥淎ssociation Between Helicopter vs Ground Emergency Medical Services and Survival for Adults With Major Trauma,鈥� by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15). Use a 0.01 significance level to test the claim that the rate of fatalities is higher for patients transported by helicopter.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Considering the test results and the actual sample rates, is one mode of transportation better than the other? Are there other important factors to consider?
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