A university administrator believes that business students are more likely to be working and going to school than their liberal arts majors.This information may lead to the business school offering courses in the evening hours while the liberal arts college maintains a daytime schedule.To test this theory, the proportion of business students who are working at least 20 hours per week is compared to the proportion of liberal arts students who are working at least 20 hours per week.A random sample of 600 from the business school has been taken and it is determined that 480 students work at least 20 hours per week.A random sample of 700 liberal arts students showed that 350 work at least 20 hours per week.The observed z for this is _______.
A)0.300
B)0.624
C)0.638
D)11.22
E)13.42

Question

Quizplus · Accepted Answer

The observed z-score is calculated using the formula for comparing two proportions. Here, the proportions of business and liberal arts students working at least 20 hours per week are compared. The calculation involves the difference in proportions, the standard error of the difference, and results in a z-score that quantifies the difference in terms of standard deviations. Given the large sample sizes and the significant difference in proportions (480/600 for business students vs. 350/700 for liberal arts students), the z-score is expected to be substantial, leading to the correct answer being a relatively high value, which is 11.22 in this case.

A University Administrator Believes That Business Students Are More Likely