Last year,KAAA's share of the 6 pm news audience was approximately equal to,but not greater than,25 percent.This station's advertising department believes the current audience share is higher than last year's 25 percent share.In an attempt to substantiate this belief,the station surveyed a random sample of 400 6 pm viewers and found that 146 watched KAAA.Calculate the appropriate test statistic to test the hypotheses.
A)-5.31
B)-4.69
C)3.21
D)4.69
E)5.31

Question

Quizplus · Accepted Answer

To test the hypothesis, we use a one-sample proportion z-test formula:
z = (p - P) / sqrt(P(1-P) / n)
where p is the observed proportion (146/400), P is the null hypothesis proportion (0.25), and n is the sample size (400).
Plugging in the values, we get:
z = (0.365 - 0.25) / sqrt(0.25 * 0.75 / 400)
z = 5.31
Therefore, the appropriate test statistic is 5.31, which is highest among the given options, and the correct answer is E.

Last Year,KAAA's Share of the 6 Pm News Audience Was