Question

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. If the value of the test statistic is 4.99 what is the conclusion of the test? Use significance level of 1%.

Select one:

A. proportions have changed significantly

B. proportions have not changed significantly

C. test is inconclusive

D. None of these alternatives is correct.

Answer 1

The test statistic value is given as 4.99. The given level of significance is 1% it means 0.01

The chi-square test for goodness of fit used to calculate test statistics value.

There are three groups so degrees of freedom for chi-square is k-1 = 3-1 =2

The chi-square table value with degrees of freedom=2 and alpha=0.01 is 9.21

It can also be obtained using excel function CHISQ.INV.RT(0.01,2) =9.21

The decision rule is, reject the null hypothesis if chi-square test statistics value is greater than the critical chi-square value.

Here test statistic value is 4.99 which is less than critical chi-square value 9.21.

Hence we fail to reject the null hypothesis and conclude that proportions have not changed significantly.

Correct answer choice is B. proportions have not changed significantly

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