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 29.1% of current readers would subscribe. The magazine contacted a simple random sample of 464 current subscribers, and 141 of those surveyed expressed interest. Test the appropriate hypotheses using a significance level of 0.05 to determine if the magazine should launch an online edition.   

H0: Select an answer p < ? > =       Ha: Select an answer p  ? < >  

?= 0.05 decision rule: reject H0 if probability > < ? ?

Test Statistic: z =   (Note: round the z-score to two decimal places - carry at least four decimal places throughout all of your calculations)

probability =   (Note: round the probability to four decimal places)

decision: Select an answer Fail to reject H? Reject H?

Conclusion: At the 0.05 level, there Select an answer is or is not  significant evidence to conclude the percentage of current subscribers who would subscribe to an online edition of the magazine is Select an answer less than different than greater than  29.1%.

Answer 1

given data

total number of subscriber (n)=464

number of people intrested (m)=141

Proportion of sucess

proportion of failure

According to question our null hypothesis will be

Claim

Assupmtion  

given

since we have assumption null pypothesis that the Probablity will be < 0.291 so

we can reject if Probablity <

Since we have

propertion of sucess

propertion of failure

probablity of getting sucess

probablity of getting failure

Number of sample (n)=464

now Z score value will be

Probablity for the respective Z score from the standard probablity table we have

now Z criticle at

Since the value will lie under the reagion of z criticle in the bell shape curve hence we can say that we dont have enough evidence to reject the so the decision is Fail to reject

Conclusion is

At the 0.05 level there is significant evidence to conclude the percentage of current subscribers who would subscribe to an online edition of the magazine is less than 29.1.