A professor wishes to discover if seniors skip more classes than do freshmen.Suppose he knows that freshmen skip 2% of their classes.He randomly samples a group of seniors.Out of 2521 classes, this group skipped 77 classes.Based on the sample, does it appear that seniors skip more than 2% of their classes? State the critical value (CV), test statistic (TS), and decision from the test.(Use α = 0.01.)
A) CV = 1.2816; TS = 3.78; reject H₀
B) CV = 2.3263; TS = 3.78; reject H₀
C) CV = 2.3263; TS = 3.08; reject H₀
D) CV = 1.2816; TS = 3.08; reject H₀

Question

Quizplus · Accepted Answer

This is a one-tailed test with a significance level of 0.01. The null hypothesis is that seniors skip the same or fewer classes than freshmen (p ≤ 0.02), and the alternative hypothesis is that seniors skip more classes than freshmen (p > 0.02). We can use a z-test since we have a large enough sample size and we know the population proportion for freshmen. The test statistic is calculated as:

TS = (phat - p) / sqrt(p*(1-p)/n)
phat = 77/2521 = 0.0305
p = 0.02
n = 2521

TS = (0.0305 - 0.02) / sqrt(0.02*(1-0.02)/2521) = 3.78

The critical value for a one-tailed test with a significance level of 0.01 is 2.3263. Since the test statistic (3.78) is greater than the critical value (2.3263), we reject the null hypothesis and conclude that seniors skip more classes than freshmen.

A Professor Wishes to Discover If Seniors Skip More Classes