Question

A book club wonders if fewer than 40 percent of students at a local university had read at least one book during the last year. To test the claim, the book club selected a random sample of students at the local university and recorded the number of students who had read at least one book during the last year. The club conducted a test with the hypotheses H0:p=0.40H0:p=0.40 versus Ha:p<0.40Ha:p<0.40. The test yielded a pp-value of 0.033. Assuming all conditions for inference were met, which of the following is an appropriate conclusion?

A) At the significance level α=0.01α=0.01, the null hypothesis is rejected. There is convincing evidence to support the claim that fewer than 40% of the students at the local university read at least one book last year.
B) At the significance level α=0.01α=0.01, the null hypothesis is rejected. There is not convincing evidence to support the claim that fewer than 40% of the students at the local university read at least one book last year.
C) At the significance level α=0.01α=0.01, the null hypothesis is not rejected. There is convincing evidence to support the claim that fewer than 40% of the students at the local university read at least one book last year.
D) At the significance level α=0.05α=0.05, the null hypothesis is rejected. There is convincing evidence to support the claim that fewer than 40% of the students at the local university read at least one book last year.
E) At the significance level α=0.05α=0.05, the null hypothesis is rejected. There is not convincing evidence to support the claim that fewer than 40% of the students at the local university read at least one book last year.

Answer 1

Explanation:

From the information given,

The null hypothesis is

H0:p = 0.40 H0:p = 0.40

The alternative hypothesis

Ha:p < 0.40 Ha:p < 0.40.

The p value of 0.033

The decision rule states that

If the significance level, α < the p value, we would accept the null hypothesis.

If the significance level, α > the p value, we would reject the null hypothesis.

From the given options,

D) At the significance level α=0.05, the null hypothesis is rejected. There is convincing evidence to support the claim that fewer than 40% of the students at the local university read at least one book last year.