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Chapter 9: Q.10.89 (page 429)
Refer to Exercise 10.83 and find a 90 % confidence interval for the difference between the mean numbers of acute postoperative days in the hospital with the dynamic and static systems.
The interval is to
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A sample size that will ensure a margin of error of at most the one specified.
Determining Sample Size The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 - a can be found by using the following expression:
Replace by n in the preceding formula (assuming that both samples have the same size) and replace each of role="math" localid="1649424190272" by 0.5 (because their values are not known). Solving for n results in this expression:
Use this expression to find the size of each sample if you want to estimate the difference between the proportions of men and women who own smartphones. Assume that you want 95% confidence that your error is no more than 0.03.
Eyewitness Accuracy of Police Does stress affect the recall ability of police eyewitnesses? This issue was studied in an experiment that tested eyewitness memory a week after a nonstressful interrogation of a cooperative suspect and a stressful interrogation of an uncooperative and belligerent suspect. The numbers of details recalled a week after the incident were recorded, and the summary statistics are given below (based on data from “Eyewitness Memory of Police Trainees for Realistic Role Plays,” by Yuille et al., Journal of Applied Psychology, Vol. 79, No. 6). Use a 0.01 significance level to test the claim in the article that “stress decreases the amount recalled.”
Nonstress: n = 40,\(\bar x\)= 53.3, s = 11.6
Stress: n = 40,\(\bar x\)= 45.3, s = 13.2
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.
Tennis Challenges Since the Hawk-Eye instant replay system for tennis was introduced at the U.S. Open in 2006, men challenged 2441 referee calls, with the result that 1027 of the calls were overturned. Women challenged 1273 referee calls, and 509 of the calls were overturned. We want to use a 0.05 significance level to test the claim that men and women have equal success in challenging calls.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Based on the results, does it appear that men and women have equal success in challenging calls?
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