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Chapter 8: Q. 9.109 (page 389)
In each of Exercises 9.107-9.112, we have provided a sample mean, sample standard deviation, and sample size. In each case, use the one-mean t-test to perform the required hypothesis test at the 5% significance level.
If thereject the null hypothesis.
Here, reject the null hypothesis.
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Testing Claims About Proportions. In Exercises 9鈥�32, 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. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Super Bowl Wins Through the sample of the first 49 Super Bowls, 28 of them were won by teams in the National Football Conference (NFC). Use a 0.05 significance level to test the claim that the probability of an NFC team Super Bowl win is greater than one-half.
Testing Claims About Proportions. In Exercises 9鈥�32, 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. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Smoking Stopped In a program designed to help patients stop smoking, 198 patients were given sustained care, and 82.8% of them were no longer smoking after one month (based on data from 鈥淪ustained Care Intervention and Post discharge Smoking Cessation Among Hospitalized Adults,鈥� by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). Use a 0.01 significance level to test the claim that 80% of patients stop smoking when given sustained care. Does sustained care appear to be effective?
Calculating Power Consider a hypothesis test of the claim that the Ericsson method of gender selection is effective in increasing the likelihood of having a baby girl, so that the claim is p>0.5. Assume that a significance level of = 0.05 is used, and the sample is a simple random sample of size n = 64.
a. Assuming that the true population proportion is 0.65, find the power of the test, which is the probability of rejecting the null hypothesis when it is false. (Hint: With a 0.05 significance level, the critical value is z = 1.645, so any test statistic in the right tail of the accompanying top graph is in the rejection region where the claim is supported. Find the sample proportion in the top graph, and use it to find the power shown in the bottom graph.)
b. Explain why the green-shaded region of the bottom graph represents the power of the test.
Estimates and Hypothesis Tests Data Set 3 鈥淏ody Temperatures鈥� in Appendix B includes sample body temperatures. We could use methods of Chapter 7 for making an estimate, or we could use those values to test the common belief that the mean body temperature is 98.6掳F. What is the difference between estimating and hypothesis testing?
Testing Claims About Proportions. In Exercises 9鈥�32, 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. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Lie Detectors Trials in an experiment with a polygraph yield 98 results that include 24 cases of wrong results and 74 cases of correct results (based on data from experiments conducted by researchers Charles R. Honts of Boise State University and Gordon H. Barland of the Department of Defense Polygraph Institute). Use a 0.05 significance level to test the claim that such polygraph results are correct less than 80% of the time. Based on the results, should polygraph test results be prohibited as evidence in trials?
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