Question

A random group of students was selected from a large student conference to analyze their class in school. Is there evidence to reject the hypothesis that the number of students is equally distributed between the four classes, at = .05?

Freshman: 9

Sophomore: 9

Junior: 15

Senior: 23

A. There is not evidence to reject the claim that students are equally distributed between the four classes because the test value 7.815 < 9.429

B. There is evidence to reject the claim that the customers' preferences are distributed between the four classes because the test value 9.488 < 9.429

C. There is not evidence to reject the claim that students are equally distributed between the four classes because the test value 9.488 < 9.429

D. There is evidence to reject the claim that students are equally distributed between the four classes because the test value 7.815 < 9.429

Answer 1

Total number of students selected = 56

Now, we want to test:

Null Hypothesis: The students are equally distributed between four classes

Alternative Hypothesis: There is an unequal distribution.

Under the Null hypothesis, each class is expected to have equal number of students. So, the expected frequency of each classes will be 56/4 = 14

We will conduct Chi-sqaure goodness of fit test to conduct the test of hypothesis.

The test-statistic is

The critical value is

As the value of test-statistic = 9.429 > 7.815, we reject the null hypothesis at 5% level of significance.

Option (D) is correct