22.19 Do our athletes graduate? The National Collegiate Athletic Association (NCAA) requires colleges to report the graduation rates of their athletes. At one large university, 78% of all students who entered in 2004 graduated within six years. One hundred thirty-seven of the 190 students who entered with athletic scholarships graduated. Consider these 190 as a sample of all athletes who will be admitted under present policies. Is there evidence that the percentage of athletes who graduate is less than 78%?

  1. (a) Explain in words what the parameter p is in this setting.

  2. (b) What are the null and alternative hypotheses H0 and Ha?

  3. (c) What is the numerical value of the sample proportion ? The P-value is the probability of what event?

  4. (d) The P-value is P = 0.033. Explain why this P-value indicates there is some reason to think that graduation rates are lower among athletes than among all students.