Question

Study was recently conducted at a major university to determine whether there is a difference in the proportion of business school graduates who go on to graduate school within five years after graduation and the proportion of non-business school graduates who attend graduate school. A random sample of 400 business school graduates showed that 70 had gone to graduate school while, in a random sample of 500 non-business graduates, 128 had gone on to graduate school.

a. Based on these sample data, and a 0.08 level of significance, conduct an appropriate test statistic?

b. What is the p-value for the test you have conducted in part "a".

Answer 1

-2.915,0.00362

Explanation:

Given that a study was recently conducted at a major university to determine whether there is a difference in the proportion of business school graduates who go on to graduate school within five years after graduation and the proportion of non-business school graduates who attend graduate school.

`H_0: p_1 = p_2\\H_a: p_1 \\eq p_2`

(Two tailed test for comparison of two proportion at 8% significance level)

we have

business school non business school proportion

70 400 0.175

100 500 0.20

p difference =-0.025

Std error of p difference
`=(p_1-p_2)/(p(1-p)((1)/(n_1) +(1)/(n_2 )) ) \\= 0.00858`

a) Z statistic = p diff/Std error =-2.915

b) p value = 0.00362

Since p <0.08 we reject null hypothesis.

There is significant difference between the two proportions.