Exhibit 11-4
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 11-4. The conclusion of the test is that the

Question

Quizplus · Accepted Answer

We can conduct a chi-square goodness-of-fit test to determine whether the observed sample proportions differ significantly from the expected population proportions.

The null hypothesis is that the sample proportions are equal to the expected population proportions, and the alternative hypothesis is that they differ.

We can calculate the expected frequencies for each college based on the expected population proportions: 
Business College: 0.35 x 300 = 105 students 
Liberal Arts College: 0.35 x 300 = 105 students 
Education College: 0.30 x 300 = 90 students

We can then calculate the chi-square statistic:

χ2 = ∑ [(observed frequency - expected frequency)^2 / expected frequency] 
χ2 = [(90-105)^2 / 105] + [(120-105)^2 / 105] + [(90-90)^2 / 90]
χ2 = 4.29

Using a chi-square distribution table with 2 degrees of freedom (3 categories -1), we find that the critical value at a 5% significance level is 5.99. Since our calculated chi-square value (4.29) is smaller than the critical value (5.99), we fail to reject the null hypothesis. Thus, we conclude that the proportions have not changed significantly.

Therefore, the best answer is B, proportions have not changed significantly.

Exhibit 11-4 In the Past, 35% of the Students at ABC University