Question

The National Collegiate Athletic Association (NCAA) requires colleges to report the graduation rates of their
athletes. Here are data from a Big Ten university's report. For parts a and b, state your hypotheses, the test
statistic and p-value, and then write a conclusion in terms of the problem.
(a) Ninety-five of the 147 athletes admitted in 1989-1991 graduated within six years.
Did the percent of athletes who graduated within six years differ significantly from the all-university
percentage, which was 70%?
(b) The graduation rates were 37 of 45 female athletes and 58 of 102 male athletes. Is there evidence that a
smaller proportion of male athletes than of female athletes graduated within six years?

Solve using Ti-83 or 84

Answer 1

a) Let p be the true proportion of athletes who graduated within six years. We want to test if the percent of athletes who graduated within six years differ significantly from the all-university percentage, which was 70%, that means we want to test if

The hypotheses are

We have the following sample information

This is a test 1 sample for proportion. The values of

are both greater than 5, we can use normal distribution as the sampling distribution of proportion. That is we can use z-test.

Enter the following in Ti-83

STAT+TESTS and 1 sample test for proportions

Enter the following

get this

The test statistics is z=-1.42

The p-value is 0.1551

We will reject the null hypothesis if the p-value is less than the significance level. Assuming a significance level of 0.05, we can see that the p-value of 0.1551 is not less than 0.05.Hence we do not reject the null hypothesis.

We fail to reject the null hypothesis.

We conclude that there is no sufficient evidence to support the claim that the percent of athletes who graduated within six years differ significantly from the all-university percentage, which was 70%.

b) Let be the true proportion of female athletes graduated within size years

be the true proportion of male athletes graduated within size years

We want to test the claim that a smaller proportion of male athletes than of female athletes graduated within six years, that is we want to test if

The hypotheses are

This is a 2 sample test for difference in proportions

We have the following sample information

Setup using Ti-83

STAT+TESTS, 2- sample test for proportions

Enter the following

get the following

The test statistics is 2.96

The p-value is 0.0015

We will reject the null hypothesis if the p-value is less than the significance level.

Here, the p-value is less than the assumed value of significance 0.05

We reject the null hypothesis.

We conclude that  there is sufficient evidence that a smaller proportion of male athletes than of female athletes graduated within six years