Question

A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it is convinced that more than 30​% of current readers would subscribe. The magazine contacted a simple random sample of 400 current​ subscribers, and 125 of those surveyed expressed interest. What should the magazine​ do?

a. What are the null and alternative​ hypotheses?

b. What is the value of the test static?

c. What is the P value of the test static?

(please show work, thanks)

Answer 1

Solution:

Given that,

= 30% = 0.30

1 - = 1 - 0.30 = 0.70

n = 400

X = 125

= X / n = 125 / 400 = 0.31

This is a right tailad test

a)

The null and alternative hypothesis is,

Ho:p = 0.30

Ha:p > 0.30

b)

The test statistics is,

z = (- ) / (1-) /n

= (0.31 - 0.30 ) / (0.30*0.70) / 400

= 0.546

P-value = P(Z > z)

= 1 - P(Z <0.546)

= 1 - 0.7075

= 0.2925