Question

A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. Find the large-sample rejection region for the test of interest to the college when using a level of significance of 0.01.

Answer 1

The rejection region is the one defined by z<-2.326.

Explanation:

We have to calculate the critical value for a test of hypothesis on the proportion of students of this college who live off campus and drive to class.

The sample is large enough, so we can use the z-statistic.

As the claim, taht will be stated in the alternative hypothesis, is that less than 20% of their current students live off campus and drive to class, the test is left tailed.

Alternative hypothesis:

`Ha: \pi<0.20`

Then, for a significance level of 0.01, 99% of the data has to be over (or 1% below) this critical z-value.

In the standard normal distribution this z-value is z=-2.326.

`P(z<-2.326)=0.01`

The critical value that divide the regions is z=-2.326. The rejection region is the one defined by z<-2.326.