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

Answer:

-2.915,0.00362

Step-by-step 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.

$H_0: p_1 = p_2\\H_a: p_1 \neq p_2$

(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 $=\frac{p_1-p_2}{p(1-p)(\frac{1}{n_1} +\frac{1}{n_2 )} } \\= 0.00858$

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.