Chapter 9: Q.11.45 (page 460)
A sample size that will ensure a margin of error of at most the one specified.
The required sample size is 1,692.
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Family Heights. In Exercises 1–5, use the following heights (in.) The data are matched so that each column consists of heights from the same family.
1. a. Are the three samples independent or dependent? Why?
b. Find the mean, median, range, standard deviation, and variance of the heights of the sons.
c. What is the level of measurement of the sample data (nominal, ordinal, interval, ratio)?
d. Are the original unrounded heights discrete data or continuous data?
Testing Claims About Proportions. In Exercises 7–22, 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
Question:Headache Treatment In a study of treatments for very painful “cluster” headaches, 150 patients were treated with oxygen and 148 other patients were given a placebo consisting of ordinary air. Among the 150 patients in the oxygen treatment group, 116 were free from head- aches 15 minutes after treatment. Among the 148 patients given the placebo, 29 were free from headaches 15 minutes after treatment (based on data from “High-Flow Oxygen for Treatment of Cluster Headache,” by Cohen, Burns, and Goads by, Journal of the American Medical Association, Vol. 302, No. 22). We want to use a 0.01 significance level to test the claim that the oxygen treatment is effective.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Based on the results, is the oxygen treatment effective?
Hypothesis Tests and Confidence Intervals for Hemoglobin
a. Exercise 2 includes a confidence interval. If you use the P-value method or the critical value method from Part 1 of this section to test the claim that women and men have the same mean hemoglobin levels, will the hypothesis tests and the confidence interval result in the same conclusion?
b. In general, if you conduct a hypothesis test using the methods of Part 1 of this section, will the P-value method, the critical value method, and the confidence interval method result in the same conclusion?
c. Assume that you want to use a 0.01 significance level to test the claim that the mean haemoglobin level in women is lessthan the mean hemoglobin level in men. What confidence level should be used if you want to test that claim using a confidence interval?
Testing Claims About Proportions. In Exercises 7–22, 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.
Denomination Effect A trial was conducted with 75 women in China given a 100-yuan bill, while another 75 women in China were given 100 yuan in the form of smaller bills (a 50-yuan bill plus two 20-yuan bills plus two 5-yuan bills). Among those given the single bill, 60 spent some or all of the money. Among those given the smaller bills, 68 spent some or all of the money (based on data from “The Denomination Effect,” by Raghubir and Srivastava, Journal of Consumer Research, Vol. 36). We want to use a 0.05 significance level to test the claim that when given a single large bill, a smaller proportion of women in China spend some or all of the money when compared to the proportion of women in China given the same amount in smaller bills.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. If the significance level is changed to 0.01, does the conclusion change?
Testing Claims About Proportions. In Exercises 7–22, 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.
Smoking Cessation Programs Among 198 smokers who underwent a “sustained care” program, 51 were no longer smoking after six months. Among 199 smokers who underwent a “standard care” program, 30 were no longer smoking after six months (based on data from “Sustained Care Intervention and Postdischarge Smoking Cessation Among Hospitalized Adults,” by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). We want to use a 0.01 significance level to test the claim that the rate of success for smoking cessation is greater with the sustained care program.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Does the difference between the two programs have practical significance?
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