Question

For each question please state your null and alternative hypothesis, your p-value and conclusion of your hypothesis test. You may use your calculator to perform the hypothesis.

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

n = 500

x = 137

= x / n = 137 / 500 = 0.274

P₀ = 0.25

1 - P₀ = 1 - 0.25 = 0.75

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.274 - 0.25 / [(0.25 * 0.75) / ]

= 1.239

Test statistic = 1.239

P(z > 1.239) = 1 - P(z < 1.239) = 1 - 0.8923 = 0.1077

P-value = 0.1077

= 0.01

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to convinced that more than 25% .