Question

In 2003, forty percent of the students at a major university were Business majors, 35% were Engineering majors and the rest of the students were majoring in other fields. In a sample of 600 students from the same university taken in 2004, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At 95% confidence, test to see whether there has been a significant change in the proportions between 2003 and 2004

Test statistic:

Explanation:

is it a

normal distribution, t distribution with 29 degrees of freedom, t-distribution with 70 degrees of freedom, Chi-square with 2 degrees of freedom, Chi-square with 1 degree of freedom

Answer 1

is it a Chi-square with 2 degrees of freedom

The following table is obtained:

Categories	Observed	Expected	(fo-fe)2/fe
Business majors	200	600*0.4=240	(200-240)2/240 = 6.667
Engineering majors	220	600*0.35=210	(220-210)2/210 = 0.476
other fields	180	600*0.25=150	(180-150)2/150 = 6
Sum =	600	600	13.143

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H_0: p_1 = 0.4, p_2 = 0.35, p_3 = 0.25

H_a​: Some of the population proportions differ from the values stated in the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

(2) Rejection Region

Based on the information provided, the significance level is \alpha = 0.05α=0.05, the number of degrees of freedom is df = 3 - 1 = 2 , so then the rejection region for this test is

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that, it is then concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level.