Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college. Refer to Exhibit 12.2.Using the p-value approach and α = 0.01,the decision and conclusion are:
A)Do not reject the null hypothesis;all proportions are equal to
B)Do not reject the null hypothesis;cannot conclude that not all of the proportions are the same
C)Reject the null hypothesis;at least one of the proportions is different from its hypothesized value
D)Reject the null hypothesis;all of the proportions are not the same

Question

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college.  Refer to Exhibit 12.2.Using the p-value approach and α = 0.01,the decision and conclusion are:
A)Do not reject the null hypothesis;all proportions are equal to 
B)Do not reject the null hypothesis;cannot conclude that not all of the proportions are the same 
C)Reject the null hypothesis;at least one of the proportions is different from its hypothesized value 
D)Reject the null hypothesis;all of the proportions are not the same

Quizplus · Accepted Answer

Using a chi-squared test with α = 0.01 and degrees of freedom = 5 - 1 = 4, we calculate a test statistic of 12.178. Looking up the p-value for this test statistic using a chi-squared table or calculator, we get a p-value < 0.01. Since the p-value is less than α, we reject the null hypothesis and conclude that at least one of the proportions is different from its hypothesized value.