Which of the following is not true when investigating two population proportions?

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?