Question

Last year, TV station KAAA had a share of the 6 p.m. news audience approximately equal to, but not greater than, 25 percent. The advertising department for the station believes the current audience share is higher than the 25 percent share they had last year. In an attempt to substantiate this belief, the station surveyed a random sample of 100 viewers of 6 p.m. news and found that 36 watched KAAA.

a) Calculate the appropriate test statistic to test the hypotheses using the critical value rule.

b) Calculate the p-value associated with the test statistic and test the claim at α = .05 using the p-value rule.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.25
Alternative Hypothesis, Ha: p > 0.25

a)
Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.36 - 0.25)/sqrt(0.25*(1-0.25)/100)
z = 2.54

As test statistic is greater than 1.64, reject the null hypothesis
There is sufficient evidence to conclude that the proportion is greater than 25 percent.

b)
P-value Approach
P-value = 0.0055

As P-value < 0.05, reject the null hypothesis.
There is sufficient evidence to conclude that the proportion is greater than 25 percent.