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 from the university 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. Using α = .05, the conclusion of the test is that the
A) null hypothesis cannot be rejected.
B) proportions have not changed significantly.
C) proportions follow normal distribution.
D) Marascuilo procedure is more applicable.

Question

Quizplus · Accepted Answer

We need to perform a chi-square goodness-of-fit test to see if the sample proportions differ significantly from the expected proportions. The null hypothesis is that the proportions have not changed. Using a significance level of .05 and degrees of freedom = 2, the critical value for the chi-square test is 5.99. The calculated chi-square value is 6, which is greater than the critical value, but not significant enough to reject the null hypothesis. Therefore, we can conclude that the proportions have not changed significantly. The Marascuilo procedure is not applicable here as we are not comparing multiple proportions.

In the Past, 35% of the Students at ABC University