A magazine is convinced that more than 24.8% of current readers would subscribe.

Question

A magazine is convinced that more than 24.8% of current readers would subscribe. random sample of 329 current subscribers, and 87 of those surveyed exp considering the launch of an online edition. The magazine plans to go ahead only if it is The magazine contacted a simple ressed interest. Test the appropriate ponleses using a significance level of 0.05 to determine if the magazine should launch an online edition. HO : 1 Select an answer , | | ? : [Select an answer V12V] decision rule: reject Ho if probabilitya Test Statistic: z decimal places throughout all of your calculations) probability decision: Select an answer Conclusion: At the 0.05 level, there Select an answer significant evidence to conclude the percentage of current subscribers who would subscribe to an online edition of the magazine is (Note: round the z-score to two decimal places - carry at least four Note: round the probability to four decimal places) - Select an answer 24.8%.

Explanation / Answer

H0 : p 0.248

Ha : p > 0.248

Here = 0.05

Decision rule : reject H0 if probability <

where Z (critical) = 1.645

Here sample size n = 329

sample proportion p^ =87/329 = 0.2644

standard proportion p0 = 0.248

standard error of proportion sep = sqrt [p^ * (1-p^)/n) = sqrt[0.248 * (1 - 0.248)/329] = 0.0238

Test statistic

z = (p^ - p0)/sep = (0.2644 - 0.248)/0.0238 = 0.69

p- value = Pr(Z > 0.69) = 0.2450

So here as p - value > 0.05 so we failed to reject the null hypothesis.

Conclusion : at the 0.05 level, there is not sufficient evidence to conclude that the percentage of current subscrivers who could subscribe to an online edition of the magzine is greater than 24.8%

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