Do more than 30% of visitors click through?

Question

A website claims that more than 30% of visitors click through to a product page. In a sample of 500 visitors, 175 click through (35%).

Run a one-sided one-proportion z-test at the 5% level (is click-through above 30%?): report the z-statistic and the decision.

Accepted Answer

Directional claim (above 30%), so use an upper-tail test. Hypotheses: H0: p = 0.30 versus H1: p 0.30. Sample proportion: \hat p = 175/500 = 0.35. Standard error under the null (p = 0.30): 	ext{SE} = \sqrt{\frac{0.30 	imes 0.70}{500}} = \sqrt{0.00042} = 0.02049. Test statistic: z = \frac{0.35 - 0.30}{0.02049} = \frac{0.05}{0.02049} = 2.44. The one-sided 5% critical value is 1.645. Since 2.44 1.645, reject H0. The one-sided p-value is 1 - \Phi(2.44) \approx 0.007. Conclusion: there is evidence the true click-through rate exceeds 30%. Takeaway. The recipe is identical across proportion tests: …

Do more than 30% of visitors click through?

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