Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is your decision if $\alpha$= 0.01?
A) Fail to reject the null hypothesis and conclude the newscast reaches about 41% of the audience.
B) Reject the null hypothesis and conclude the newscast does not reach 41% of the audience.
C) Fail to reject the alternate and conclude the newscast does not reach 41% of the audience.
D) Reject the alternate and conclude the newscast reaches about 41% of the audience.

Question

Quizplus · Accepted Answer

The null hypothesis is that the proportion of viewers who watch the late evening news on the local CBS station is equal to or less than 41%, and the alternate hypothesis is that it is greater than 41%. 
As the significance level, α = 0.01 is given, we can perform a one-tailed z-test to find the p-value:

z = (0.36 - 0.41) / √(0.41 * 0.59 / 100) = -1.51

Using a standard normal table, the p-value is p = P(Z < -1.51) = 0.0655.

Since the p-value (0.0655) is greater than α (0.01), we fail to reject the null hypothesis. Thus, we can conclude that the newscast reaches about 41% of the audience. Therefore, the best choice is A.

Based on the Nielsen Ratings, the Local CBS Affiliate Claims α\alphaα

Based on the Nielsen Ratings, the Local CBS Affiliate Claims $\alpha$