Question

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. 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 α = 0.01?

a. Fail to reject the null hypothesis.

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.

Answer 1

a. Fail to reject the null hypothesis.

Explanation:

Here we test the claim that proportion of reachers is really 41%

`H_0: p =0.41\\H_a: p \\eq 0.41`

(Two tailed test at 1% significance level)

Observed proportion = 0.36

Sample size n = 100

Std error of proportion =
`\sqrt{(pq)/(n) } \\=\sqrt{(0.41*0.59)/(100) } \\=0.0492`

p difference = 0.36-0.41 =- 0.05

Test statistic Z = p diff/std error =-1.0166

p value=0.286

Since p >0.01 we accept null hypothesis.

a. Fail to reject the null hypothesis.