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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.

Respuesta :

Answer:

a. Fail to reject the null hypothesis.

Step-by-step explanation:

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

[tex]H_0: p =0.41\\H_a: p \neq 0.41[/tex]

(Two tailed test at 1% significance level)

Observed proportion = 0.36

Sample size n = 100

Std error of proportion = [tex]\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.41*0.59}{100} } \\=0.0492[/tex]

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.

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