The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 200 business students were randomly sampled and 65 have laptops. Find the rejection region for the corresponding test using $\alpha = .01$

Question

The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 200 business students were randomly sampled and 65 have laptops. Find the rejection region for the corresponding test using $$\alpha = .01$$ A) Reject $H _ { 0 }$ if $z = 2.33$. B) Reject $H _ { 0 }$ if $z < - 2.33$. C) Reject $H _ { 0 }$ if $z > 2.575$ or $z < - 2.575$. D) Reject $H _ { 0 }$ if $z > 2.33$.

Quizplus · Accepted Answer

The null hypothesis $H_0$ is that the proportion is 25% or less. Since the alternative hypothesis is that the proportion exceeds 25%, this is a right-tailed test. At $\alpha = 0.01$, the critical value for a right-tailed test is $z = 2.33$. Therefore, reject $H_0$ if $z > 2.33$.

The Business College Computing Center Wants to Determine the Proportion α=.01\alpha = .01α=.01

The Business College Computing Center Wants to Determine the Proportion $\alpha = .01$