A recent study by the Pew Research Center reported that 76% of American adults ages 18 and older said that they read at least one book in the past year. A majority of adults reported that they prefer to read books in print over an e-book or listening to an audiobook. How does this book preference compare across two different age groups, adults ages 18-29 years old and adults ages 50-64 years old?

Let p1 represent the population proportion of American adults ages 18-29 who prefer to read printed books over any other form of books, and p2represent the population proportion of American adults ages 50-64 who prefer to read printed books over any other form of books.

To estimate the difference in the population proportions, p1 - p2, a random sample of 300 American adults ages 18-29 and a random sample of 350 American adults ages 50-64 were selected and asked if they prefer to read printed books over any other form of books. The results are summarized below:

1 = American adults 2 = American adults
ages18-29 ages 50-64
Sample Size 300 350
Number prefering printed books-
over any other form of books 219 231
Proportion prefering printed books-
over any other form of books 0.73 0.66

(a) Provide a 90% confidence interval to estimate the difference in the population proportion of American adults ages 18-29 who prefer to read printed books over any other form of books less the population proportion of American adults ages 50-64 who prefer to read printed books over any other form of books.

(b) Which of the following interpretation(s) is (are) an appropriate interpretation for the 90% confidence level, in context?

a. If we repeated this procedure many times and for each repetition, we computed the 90% confidence interval, we would expect 90% of the resulting intervals would contain the difference in the sample proportion of American adults ages 18-29 who prefer to read printed books over any other form of books less the sample proportion of American adults ages 50-64 who prefer to read printed books over any other form of books.
b. If we repeated this procedure many times and for each repetition, we computed the 90% confidence interval, we would expect 90% of the resulting intervals would contain the difference in the population proportion of American adults ages 18-29 who prefer to read printed books over any other form of books less the population proportion of American adults ages 50-64 who prefer to read printed books over any other form of books.
c. If we repeated this procedure many times and for each repetition, we computed the 90% confidence interval, we would expect the resulting interval to contain the difference in the population proportion of American adults ages 18-29 who prefer to read printed books over any other form of books less the population proportion of American adults ages 50-64 who prefer to read printed books over any other form of books with a probability of 0.90.

(c) A 95% confidence interval based on the same data would result in an interval that is the 90% confidence interval.

A. wider than
B. narrower than
C. the same width as