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 90 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 No

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

A. H0​: pequals0.2 HA​: pgreater than0.2

B. H0​: pequals0.2 HA​: pless than0.2

C. H0​: pequals0.2 HA​: pnot equals0.2

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. zequals 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-valueequals nothing ​(Round to four decimal places as​ needed.)

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

What is your​ conclusion? Choose the correct answer below.

A. Since the​ P-value was low​, reject H0.

B. Since the​ P-value was high​, fail to reject H0.

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

What should the company​ do? Choose the correct answer below.

A) The survey results would not be useful if less than 20% of the current readers were interested. The company should bot launch the online edition.

B) The survey results would be highly unusual if less than 20% of the current readers were interested. The company should not launch the online edition.

C) The survey results would not be unusual if less than %20 of the current readers were interested. The company should launch the online edition.

D) The assumptions and conditions are not met, so the test is not valid.

Answer 1

Answer :

we have given :

n = sample size = 400

x = 90 of those surveyed expressed interest

phat = sample proportion = x / n = 90 / 400 = 0.225

p = population proportion =   20 % = 0.20

Claim :

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

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

Answer : Yes

for one sample prorportion z test : condtion of np > 10 and nq > 10

where q = 1 - p

here np = 400 * 0.20 = 80

and nq = 400 * 0.80 = 320

here np > 10 and nq > 10 condition satisfy we can do test

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

Answer : correct option A

A. H0​: p equals 0.2 HA​: p greater than 0.2 ( claim )

( it is one tailed , right tailed test )

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

Answer : correct option is A

A. z equals =  z = ( phat - p ) / SQRT( p * (1-p) / n)

z = ( 0.225 - 0.20 ) / SQRT( 0.20 * (1- 0.20 ) / 400 )

z = 0.025 / 0.02  

z = 1.25

## Find the​ P-value. Select the correct choice below​ and, if​ necessary,

fill in the answer box to complete your choice.

Answer : correct option is A

A. ​P-valueequals

p value = P ( z > 1.25 ) now use statistical table  

= 0.10565 ie 0.1057

= 0.1057

## Decision :

we reject Ho if p value is less than  α value using p value approach here p value is

greater than  α value we fail to reject Ho at given level of significance .

## What is your​ conclusion? Choose the correct answer below.

Answer : Correct option B

B. Since the​ P-value was high​, fail to reject H0.

We accpet Ho that is   p = 0.20 our claim not satisfy ,

and in words : Correct option is A

A) The survey results would not be useful if less than 20% of the current readers were interested. The company should not launch the online edition.