Question

Help with hypothesis testing!
A magazine is considering the launch of an online edition. The magazine will only go ahead with the launch if convinced that more than 25% of its current subscribers would subscribe. The magazine takes a simple random sample of 500 current subscribers and 137 express interest in the online version. Is there evidence that more than 25% of the magazine's current subscribers would subscribe to an online edition? Use a 5% significance level.

Calculate the appropriate test-statistic for this test.

Answer 1

You'll use this formula

\[\Large z = \frac{\hat{p} - p}{SE}\]

where

\[\Large \text{Sample Proportion} =\hat{p} = \frac{137}{500} = 0.274\]
\[\Large \text{Population Proportion} = p = 0.25\]
\[\Large \text{Sample Size} = n = 500\]

Answer 2

Also,
\[\Large \text{Standard Error} = SE = \sqrt{\frac{p(1-p)}{n}}\]
\[\Large SE = \sqrt{\frac{0.25(1-0.25)}{500}}\]
\[\Large SE \approx 0.0193649\]

Answer 3

I'll let you finish up. Let me know what you get or if you need more help.