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. The calculated value for the test statistic equals
A) .01.
B) .75.
C) 4.29.
D) 4.38.

Question

Quizplus · Accepted Answer

The test statistic for a chi-square test for goodness of fit can be calculated using the formula: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. Given the proportions, the expected frequencies for Business, Liberal Arts, and Education are 105 (35% of 300), 105 (35% of 300), and 90 (30% of 300), respectively. Plugging in the observed frequencies (90 for Business, 120 for Liberal Arts, and 90 for Education), the calculation is as follows: $\chi^2 = \frac{(90-105)^2}{105} + \frac{(120-105)^2}{105} + \frac{(90-90)^2}{90} = \frac{225}{105} + \frac{225}{105} + 0 = 4.29$.

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