What conditions are necessary to use the z-test for testing the difference between two population proportions?

Confounding Variables A pharmaceutical company has applied for approval to market a new arthritis medication. The research involved a test group that was given the medication and another test group that was given a placebo. Describe some possible confounding variables that could influence the results of the study.

In Exercises 25–28, determine whether a normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions p1 and p2 at the level of significance α. Assume the samples are random and independent.

Claim: p1<p2; α=0.05

Sample statistics: x1 = 86, n1=900 and x2 = 107, n2 = 1200

Constructing Confidence Intervals for p1-p2 You can construct a confidence interval for the difference between two population proportions p1-p2 by using the inequality below.

[Image] Complicated mathematical formula.

In Exercises 23–26, construct the indicated confidence interval for p1-p2. Assume the samples are random and independent.

Critical Threats Repeat Exercise 25 but with a 99% confidence interval. Describe the likelihood that equal proportions of the population see cyberterrorism and the spread of infectious diseases as critical threats in the next 10 years.

Constructing Confidence Intervals for p1-p2 You can construct a confidence interval for the difference between two population proportions p1-p2 by using the inequality below.

In Exercises 23–26, construct the indicated confidence interval for p1-p2. Assume the samples are random and independent.

Students Planning to Study Visual and Performing Arts In a survey of 10,000 students taking the SAT, 7% were planning to study visual and performing arts in college. In another survey of 8000 students taken 10 years before, 8% were planning to study visual and performing arts in college. Construct a 95% confidence interval for p1-p2, where p1 is the proportion from the recent survey and p2 is the proportion from the survey taken 10 years ago. (Adapted from College Board)

Young Adults In a survey of 3500 males ages 20 to 24 whose highest level of education is some college, but no bachelor’s degree, 80.2% were employed. In a survey of 2000 males ages 20 to 24 whose highest level of education is a bachelor’s degree or higher, 86.4% were employed. At α=0.01, can you support the claim that there is a difference in the proportion of those employed between the two groups? (Adapted from National Center for Education Statistics)

Seat 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