Question

A report suggests that business majors spend the least amount of time on course work than do all other college students. A provost of a university conducts a survey of 50 business and 50 nonbusiness students. Students are asked if they study hard, defined as spending at least 20 hours per week on course work. The response shows “yes” if they study hard or “no” otherwise; the responses are shown in the accompanying table as well as the accompanying Excel file. (You may find it useful to reference the appropriate table: z table or t table)

Business Majors Non-business Majors Business Majors Non-business Majors
Yes No No No
No Yes No No
No Yes No No
No No No Yes
No No No No
No No No No
No No No Yes
No Yes No No
No No No No
Yes Yes No Yes
No Yes No No
No No No Yes
No Yes No No
No Yes Yes Yes
No Yes No No
Yes No No Yes
No No No No
No No No No
No No No No
No Yes No No
Yes Yes No No
No No Yes No
No No No No
No No Yes No
No No Yes Yes Calculate the value of the test statistic.

Answer 1

The test statistic for comparing the study habits of business and non-business majors is -1.63.

Step-by-step explanation:

To calculate the test statistic, we need to use the formula for a two-sample proportion z-test.

The test statistic is given by:

z = (p1 - p2) / sqrt((p_bar * (1 - p_bar) / n1) + (p_bar * (1 - p_bar) / n2))

where p1 and p2 are the proportions of business and non-business students who study hard, p_bar is the pooled proportion, n1 and n2 are the sample sizes.

In this case, the proportions are:

p1 = 7/50 = 0.14

p2 = 9/50 = 0.18

And the sample sizes are:

n1 = 50

n2 = 50

Substituting these values into the formula, we get:

z = (0.14 - 0.18) / sqrt((0.14 * (1 - 0.14) / 50) + (0.14 * (1 - 0.14) / 50))

Calculating this expression gives a test statistic of approximately -1.63.