Question

23.26 Do our athletes graduate? Return to the study in Exercise 22.19 (page 530), which found that 149 of 190 athletes admitted to a large university graduated within 6 years. This did not differ significantly (P=0.0968) from the 82% graduation rate for all students at the university.

1. It may be more informative to give a 95% confidence interval for the graduation rate of athletes. Construct this confidence interval.
2. Is the 82% graduation rate for all students included in your confidence interval? Explain why you are or are not surprised by this.
3. Suppose that 784 of an SRS of 1000 athletes admitted to a large university graduated within 6 years. In this situation, the results would differ significantly (P<0.001) from the 82% graduation rate for all students at the university. Why are these results statistically significant when the sample proportion based on the sample of size 1000 and the sample proportion based on the sample of size 190 are both 0.784?

Answer 1

p = 149/190 = 0.78

The 95% confidence interval will be:

= p ± z*(√p(1-p)/n)

= 0.78 ± 1.96*(√0.78(1-0.78)/190)

= (0.7257, 0.8427)

The 95% confidence interval for the graduation rate of athletes is between 0.7257 and 0.8427.

Yes, the 82% graduation rate for all students included is in the confidence interval.

These results are statistically significant when the sample proportion based on the sample of size 1000 and the sample proportion based on the sample of size 190 are both 0.784 because we are 95% confident that the true graduation rate of athletes is between 0.7257 and 0.8427.