A magazine is considering the launch of an online edition. The magazine plans to

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 104 of those surveyed expressed interest. What should the company do? Test appropriate hypotheses and state your conciliation. Are the assumptions and the conditions to perform a one-proportion z-test met? no yes State the null and alternative hypotheses. Choose the correct answer below H_0; p = 0.91 H_A; p 0.91 H_0; p = 0.91 H_A; p notequalto 0.91 The assumptions and conditions are not met, so the test cannot proceed. Determine the z-test statistic. Select the correct choice below end, if necessary fill in the answer box to complete your choice. Z = 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 P-value = The assumptions and conditions are not met, so the test cannot proceed. Do the result the survey cast doubt on the airline's claim? Explain. Choose the correct answer below. No since the null hypothesis is not rejected Yes, since the null hypothesis in rejected. Yes, since the null hypothesis is rejected. No, since the null hypothesis is rejected. The assumptions and conditions are not met, so the test cannot proceed.

Explanation / Answer

Solution:-

x = 88, n = 168

p = 88/168 = 0.5238

P = 91/100 = 0.91

a) Yes, the assumptions and conditions to perform a one proportion z-test ia met.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.91

Alternative hypothesis: P 0.91

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.02208

z = (p - P) /

z = -17.49

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -17.49 or greater than 17.49.

Thus, the P-value = 0.00001

Interpret results. Since the P-value (0.00001) is less than the significance level (0.05), we have to reject the null hypothesis.

We do not have significant evidence in the favor of airlines claim.

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