Question

A 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

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p > 0.25

= x / n = 137 / 500 = 0.274

P₀ = 0.25

1 - P₀ = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.274 - 0.25 (0.25 * 0.75) / 1160

= 1.24

P(z >1.24) = 1 - P(z < 1.24) = 1 - 0.8925

P-value = 0.1075

= 0.01

P-value >

Fail to reject the null hypothesis .