Question: A July 2009 Pew Research Center survey asked a variety of science questions of independent random samples of scientists and the public at-large (https://people-press.org/report/528/). One of the questions asked was whether all parents should be required to vaccinate their children. The percentage of people answering "yes" to this question was 69% of the general public and 82% of scientists. Suppose that the survey included 110 members of the general public and 105 scientists.
a. Construct a 98% confidence interval for the difference between the two population proportions.
b. Using the 1% significance level, can you conclude that the percentage of the general public who feels that all parents should be required to vaccinate their children is less than the percentage of all scientists who feels that all parents should be required to vaccinate their children? Use the critical-value and p-value approaches.
c. The actual sample sizes used in the survey were 2001 members of the general public and 1005 scientists. Repeat parts a and b using the actual sample sizes. Does your conclusion change in part b?