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. Suppose a sample of 108 students produced a test statistic of $z = - 1.35$. Find the $p$-value for the test of interest to the college.
A) $p = 0.0885$
B) $p = 0.1770$
C) $\mathrm { p } = 0.4115$
D) $\mathrm { p } = 0.9115$

Question

Quizplus · Accepted Answer

The p-value for a z-test statistic of -1.35, when testing if the proportion is less than a specified value, is found by looking up the cumulative probability of Z < -1.35 in the standard normal distribution table or using a calculator. This gives a p-value of approximately 0.0885, indicating the probability of observing a test statistic as extreme as -1.35 or more extreme, under the null hypothesis.

A Small Private College Is Interested in Determining the Percentage 20%20 \%20%

A Small Private College Is Interested in Determining the Percentage $20 \%$