In each of the following cases, we wish to test the null hypothesis H₀: $\mu$ =18. In which case can this null hypothesis be rejected at a significance level $\alpha$ = 0.05? A) 95% confidence interval for $\mu$ is (16 to 21), H_a: $\mu$ $\neq$ 18. B) 90% confidence interval for $\mu$ is (15 to 20), H_a: $\mu$ 18. D) 90% confidence interval for $\mu$ is (15 to 22), H_a: $\mu$ $\neq$ 18.

Question

In each of the following cases, we wish to test the null hypothesis H₀: $\mu$ =18. In which case can this null hypothesis be rejected at a significance level $\alpha$ = 0.05? A) 95% confidence interval for $\mu$ is (16 to 21), H_a: $\mu$ $\neq$ 18. B) 90% confidence interval for $\mu$ is (15 to 20), H_a: $\mu$ < 18. C) 90% confidence interval for $\mu$ is (19 to 26), H_a: $\mu$ > 18. D) 90% confidence interval for $\mu$ is (15 to 22), H_a: $\mu$ $\neq$ 18.

Quizplus · Accepted Answer

In option C, the 90% confidence interval for $\mu$ is (19 to 26), which does not include the null hypothesis value of 18. This means we can reject the null hypothesis at the 0.05 significance level because the interval suggests $\mu$ is greater than 18.

In Each of the Following Cases, We Wish to Test μ\muμ

In Each of the Following Cases, We Wish to Test $\mu$