A streaming music site changed its format to focus on previously unreleased music from rising artists. The site manager now wants to determine whether the number of unique listeners per day has changed. Before the change in format, the site averaged 131,520 unique listeners per day. Now, beginning three months after the format change, the site manager takes a random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. The manager finds that the p-value for the hypothesis test is approximately 0.0743.

What can be concluded at the 95% confidence level?

(A) The manager should reject the null hypothesis; there is sufficient evidence that the number of unique daily listeners has likely changed.
(B) The manager should reject the null hypothesis; there is not enough evidence to conclude that the number of unique daily listeners has changed.
(C) The manager should fail to reject the null hypothesis; there is sufficient evidence that the number of unique daily listeners has likely changed.
(D) The manager should fail to reject the null hypothesis; there is not enough evidence to conclude that the number of unique daily listeners has changed.

D) The manager should fail to reject the null hypothesis; there is not enough evidence to conclude that the number of unique daily listeners has changed.

Step-by-step explanation:

The scenario indicates the null hypotheses and alternative hypotheses are

Null hypotheses: The number of unique daily listeners hasn't changed.

Alternative hypotheses: The number of unique daily listeners has changed.

The null hypothesis is rejected if the calculated p-value is less significance level.

We are given that p-value is 0.0743 and confidence level=0.95.

Significance level =α=1-0.95=0.05.

As we can see the p-value is greater than significance level, so, we fail to reject the null hypotheses at 5% significance level.

Thus, we conclude at the 95% confidence level that the manager should fail to reject the null hypothesis; there is not enough evidence to conclude that the number of unique daily listeners has changed