For the given binomial sample size and null-hypothesized value of $\mathrm { P } 0 ,$ determine whether the sample size is large
enough to use the normal approximation methodology to conduct a test of the null hypothesis $\mathrm { H } _ { 0 } : \mathrm { p } " \mathrm { P } 0$
-The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds $30 \%$ , then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 75 have laptops. Find the rejection region for the corresponding test using $\alpha = .05$ .

Question

For the given binomial sample size and null-hypothesized value of

\mathrm { P } 0 ,

determine whether the sample size is large
enough to use the normal approximation methodology to conduct a test of the null hypothesis

\mathrm { H } _ { 0 } : \mathrm { p } " \mathrm { P } 0

-The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds

30 \%

, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 75 have laptops. Find the rejection region for the corresponding test using

\alpha = .05

.

Quizplus · Accepted Answer

The normal approximation can be used because the sample size is large enough (np and n(1-p) are both greater than 5). For a one-tailed test with $\alpha = .05$, the critical z-value is 1.645. Since the alternative hypothesis suggests looking for a proportion greater than 30%, we reject $H_0$ if $z > 1.645$.

For the Given Binomial Sample Size and Null-Hypothesized Value Of \mathrm