Exhibit 12-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
-Refer to Exhibit 12-4. The conclusion of the test is that the
A)proportions have changed significantly
B)proportions have not changed significantly
C)test is inconclusive
D)None of these alternatives is correct.

Question

Quizplus · Accepted Answer

To test whether the proportions have changed significantly, we can use a chi-square goodness-of-fit test. After calculating the expected frequencies for each college based on the assumption that the proportions have not changed, the computed chi-square value is 3.33 with 2 degrees of freedom, which has a p-value of 0.189. Since this p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis and conclude that the proportions have not changed significantly. Therefore, the best choice is B.

Exhibit 12-4 In the Past, 35% of the Students at ABC University