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%.

A. proportions have changed significantly
B. proportions have not changed significantly
C. test is inconclusive
D. None of these alternatives is correct.

Answer 1

Proportions have not changed significantly ( B )

Explanation:

GIVEN DATA :

Test statistic = 4.99

significance level = 1% = 0.01

k ( number of groups ) = 3

will we use the chi-squared test to determine the degree of freedom

which is : k-1 = 3 - 1 = 2

looking at the chi-square table to determine the critical value of the test

at significance level = 0.01 and degree of freedom = 2 the critical value = 9.21

Comparing the test value ( 4.99 ) and the critical value ( 9.21 ) it can seen that the test value < critical value which is a condition for not rejecting null hypothesis of the test.

therefore we won't reject the null hypothesis