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 20​% of current readers would subscribe. The magazine contacted a simple random sample of 400 current​ subscribers, and 102 of those surveyed expressed interest. What should the company​ do? Test appropriate hypotheses and state your conclusion.

Are the assumptions and the conditions to perform a​ one-proportion z-test​ met?

Yes or No

State the null and alternative hypotheses. Choose the correct answer below.

A. H0​: p equals=0.20.2

HA​: p not equals≠0.20.2

B. H0​:p equals=0.20.2

HA​:p less than<0.20.2

C. H0​:p equals=0.20.2

HA​: p greater than>0.20.2

D.The assumptions and conditions are not​ met, so the test cannot proceed.

Determine the​ z-test statistic. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. z equals=nothing

​(Round to two decimal places as​ needed.)

B. The assumptions and conditions are not​ met, so the test cannot proceed.

Find the​ P-value. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. ​P-value equals=nothing

​(Round to four decimal places as​ needed.)

B. The assumptions and conditions are not​ met, so the test cannot proceed.

Answer 1

Given,

p : proportion of current readers would subscribe

Hypothesized proportion of current readers would subscribe : p_o = 20/100 = 0.20

The magazine plans to go ahead only if it is convinced that more than 20​% of current readers would subscribe i.e if p >0.20

Sample size : n= 400

Number current​ subscribers who expressed interest : x = 102

Sample Proportion of subscribers who expressed interest : = x/n = 102/400= 0.255

= 1- = 1-0.255 = 0.745

As n = 102 > and n= 298 > 5 ; The assumptions and the conditions to perform a ​one-proportion z-test​ are met

Are the assumptions and the conditions to perform a​one-proportion z-test​ met?

Yes

State the null and alternative hypotheses. Choose the correct answer below.

C. H_o​:p=0.2

H_A​: p >0.2

Right Tailed test

Determine the​ z-test statistic

z-test statistic = 2.75

A. z equals= 2.75

Find the​ P-value.

For right tailed test

p-value = 0.003

A. ​P-value equals=0.003