Question

magazine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacts a simple random sample of 500 current subscribers, and 137 of those surveyed expressed interest. What should the company do? Carry out a hypothesis test at the .01 significance level.

Answer 1

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

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.274 - 0.25)/sqrt(0.25*(1-0.25)/500)
z = 1.24

P-value Approach
P-value = 0.1075
As P-value >= 0.01, fail to reject null hypothesis.

The magazine should not go ahead