A statistics question requires a significance test with null hypothesis H_0: p =

Question

A statistics question requires a significance test with null hypothesis H_0: p = 0.3, where p is a population proportion. Two students, Juan and Tamara, both do the question, and they both calculate the correct positive value of the z-statistic. However, Juan performs a one-tailed test (using the alternative hypothesis H_a: p > 0.3), and Tamara performs a two-tailed test (using the alternative hypothesis H_a: p notequalto 0.3). Given that both students are correct in their work, which of the following is NOT possible? (A) Both students reject the null hypothesis at the 0.05 significance level. (B) Both students fail to reject the null hypothesis at the 0.05 significance level. (c) Juan rejects the null hypothesis at the 0.05 significance level and Tamara fails to reject the null hypothesis at the 0.05 significance level. (d) Juan fails to reject the null hypothesis at the 0.05 significance level and Tamara rejects the null hypothesis at the 0.05 significance level. (e) Juan fails to reject the null hypothesis at the 0.01 significance level and Tamara rejects the null hypothesis at the 0.05 significance level.

Explanation / Answer

The p-value of two tailed test is double the p-value of one tailed test.

Tamara-p-value =2*(Jaun-p-value)

Jaun reject the null hypothesis at 0.05 level of significance means p-value for two tailed test is less than 0.05. That is p-value of one tailed test is also less than 0.05. So Tamara must reject the null hypothesis at 0.05 level of signficance.

So option C is not possible.

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