A recent study by the Pew Research Center reported that 76% of American adults a
ID: 3048629 • Letter: A
Question
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.a
1 point(s)
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.
1.b
1 point(s)
Which of the following interpretation(s) is (are) an appropriate interpretation for the 90% confidence level, in context?
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.
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.
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 probablity of 0.90.
1.c
1 point(s)
A 95% confidence interval based on the same data would result in an interval that is ___________ the 90% confidence interval.
wider than
narrower than
the same width as
1.d
1 point(s)
The computation of the 90% confidence interval, which involved using a z* multiplier, requires that some assumptions are met. State all the assumptions that are required for this inference procedure.
This interval requires that the population proportions are based on independent random samples from two populations.
This interval requires that the sample proportions are based on independent random samples from two populations.
This interval requires that the population of differences in proportions follows a normal distribution.
This interval requires that all quantiaties n1p1, n1(1-p1), n2p2 and n2(1-p2) are at least 10
This interval requires that n1 and n2 are large enough, that is, that both sample sizes are at least 25.
1.e
1 point(s)
If we decide to test the hypotheses H0: p1 = p2 versus Ha: p1 p2, what will our decision be at the 10% level, using the results of our 90% confidence interval?
Reject the null hypothesis
Fail to reject the null hypothesis
Cannot tell
1 = American adults ages 18-29 2 = American adults 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 0.66Explanation / Answer
a) The pooled sample proportion P = (p1 * n1 + p2 * n2)/(n1 + n2)
= (0.73 * 300 + 0.66 * 350)/(300 + 350)
= 0.69
SE = sqrt(P * (1 - P) * (1/n1 + 1/n2))
= sqrt(0.69 * 0.31 * (1/300 + 1/350))
= 0.036
At 90% confidence interval the critical value is z0.95 = 1.645
The interval is
(p1 - p2) +/- z0.05 * SE
= (0.73 - 0.66) +/- 1.645 * 0.036
= 0.07 +/- 0.059
= 0.011, 0.129
b) Option - A
c) wider than 90% confideb=nce interval
d) Option -B, C
e) As the interval doesn't contain the hypothised value 0, so the null hypothesis is rejected.
Option - A) reject null hypothesis