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 calculated value for the test statistic equals
A)0.01
B)0.75
C)4.29
D)4.38

Question

Quizplus · Accepted Answer

To test whether the proportions have changed, we will use a chi-square goodness-of-fit test.

First, we need to calculate the expected frequencies for each college if the proportions are still 35%, 35%, and 30% respectively.

Expected frequency for Business College = 0.35 x 300 = 105 
Expected frequency for Liberal Arts College = 0.35 x 300 = 105 
Expected frequency for Education College = 0.30 x 300 = 90

To calculate the test statistic:

((observed frequency - expected frequency)^2 / expected frequency)

For Business College: ((90-105)^2 / 105) = 2.14 
For Liberal Arts College: ((120-105)^2 / 105) = 2.14 
For Education College: ((90-90)^2 / 90) = 0

The total test statistic is the sum of these values:

2.14 + 2.14 + 0 = 4.29

Therefore, the calculated value for the test statistic equals 4.29, which is choice C.

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