BackSeat Belt Use In a survey of 1000 drivers from the West, 934 wear a seat belt. In a survey of 1000 drivers from the Northeast, 909 wear a seat belt. At α=0.05, can you support the claim that the proportion of drivers who wear seat belts is greater in the West than in the Northeast? (Adapted from National Highway Traffic Safety Administration)
Parks and Mental Health In Exercises 13–18, use the figure, which shows the percentages from a survey of two hundred 18- to 24-year-olds in the United States who say that various park and recreation activities have a positive impact on their mental health. (Adapted from National Recreation and Park Association)
Exercising and Taking Classes At α=0.01, can you reject the claim that the proportion of 18- to 24-year-olds who benefit mentally from exercising in parks is greater than or equal to the proportion who benefit mentally from taking classes in parks?
In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions and at the level of significance . Assume the samples are random and independent.
Claim: p1≠p2, α=0.01
Sample statistics: x1=35, n1=70, and x2=36, n2=60
Testing the Difference Between Two Proportions In Exercises 7–12, (a) identify the claim and state Ho and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent.
Multiple Sclerosis Drug In a study to determine the effectiveness of using a drug to treat multiple sclerosis, 488 subjects were given the drug and 244 subjects were given a placebo. The numbers of subjects who had 12-week confirmed disability progression were tracked. The results are shown at the left. At α=0.01, can you support the claim that there is a difference in the proportion of subjects who had no 12-week confirmed disability progression? (Adapted from The New England Journal of Medicine)
Parks and Mental Health In Exercises 13–18, use the figure, which shows the percentages from a survey of two hundred 18- to 24-year-olds in the United States who say that various park and recreation activities have a positive impact on their mental health. (Adapted from National Recreation and Park Association)
Taking Classes and Enjoying Nature At α=0.05, can you support the claim that the proportion of 18- to 24-year-olds who benefit mentally from taking classes in parks is less than the proportion who benefit mentally from enjoying nature in parks?
Parks and Mental Health In Exercises 13–18, use the figure, which shows the percentages from a survey of two hundred 18- to 24-year-olds in the United States who say that various park and recreation activities have a positive impact on their mental health. (Adapted from National Recreation and Park Association)
Socializing and Taking Classes At α=0.05, can you support the claim that the proportion of 18- to 24-year-olds who benefit mentally from socializing in parks is different from the proportion who benefit mentally from taking classes in parks?
In Exercises 29 and 30, (a) identify the claim and state Ho and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent.
A medical research team conducted a study to test the effect of a drug used to treat a type of inflammation. In the study, 68 subjects took the drug and 68 subjects took a placebo. The results are shown below. At α=0.05, can you reject the claim that the proportion of subjects who had at least 24 weeks of accrued remission is the same for the two groups? (Source: The New England Journal of Medicine)
Daily Activities In Exercises 19–22, the results of a survey of 200 U.S. randomly selected U.S. men and 300 randomly selected U.S. women are shown in the figure at the left, which displays the percentages engaged in working or socializing and communicating on an average day. (Adapted from U.S. Bureau of Labor Statistics)
Women’s Activities At α=0.01, can you reject the claim that the proportion of women who work is the same as the proportion of women who socialize and communicate on an average day?
For , test the claim that for using...
(A) A Hypothesis Test.
For , test the claim that for using ...
(B) Confidence Interval
The General Social Survey regularly asks individuals to disclose their religious affiliation. The following data represent the religious affiliation of young adults, aged 18 to 29, in the 1970s, 1980s, 1990s, and 2000s. Do the data suggest different proportions of 18- to 29-year-olds have been affiliated with religion in the past four decades? Use the α = 0.05 level of significance.
"Determining Sample Size An educator wants to determine the difference between the proportion of males and females who have completed four or more years of college. What sample size should be obtained if she wishes the estimate to be within 2 percentage points with 90% confidence, assuming that
b. she does not use any prior estimates?"
"Putting It Together: Salk Vaccine On April 12, 1955, Dr. Jonas Salk released the results of clinical trials for his vaccine to prevent polio. In these clinical trials, 400,000 children were randomly divided in two groups. The subjects in group 1 (the experimental group) were given the vaccine, while the subjects in group 2 (the control group) were given a placebo. Of the 200,000 children in the experimental group, 33 developed polio. Of the 200,000 children in the control group, 115 developed polio.What type of experimental design is this?
b. What are the treatments?"
"Putting It Together: Salk Vaccine On April 12, 1955, Dr. Jonas Salk released the results of clinical trials for his vaccine to prevent polio. In these clinical trials, 400,000 children were randomly divided in two groups. The subjects in group 1 (the experimental group) were given the vaccine, while the subjects in group 2 (the control group) were given a placebo. Of the 200,000 children in the experimental group, 33 developed polio. Of the 200,000 children in the control group, 115 developed polio.What type of experimental design is this?
e. Does it appear to be the case that the vaccine was effective?"
Why do we use a pooled estimate of the population proportion when testing a hypothesis about two proportions? Why do we not use a pooled estimate of the population proportion when constructing a confidence interval for the difference of two proportions?