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 500 current​ subscribers, and 175 of those surveyed expressed interest. What should the company​ do? Test appropriate hypotheses and state your conclusion.

Z test statistic

Z=

P value=

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.30

Ha : p > 0.30

n = 500

x = 175

= x / n = 175 / 500 = 0.35

P0 = 0.30

1 - P0 = 1-0.30=0.70

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.35 -0.30 / [(0.30*0.70) / 500]

= 2.44

Test statistic = z = 2.44

P(z >2.44 ) = 1 - P(z < 2.44 ) = 1 - 0.9927

P-value = 0.0073