over the past ten years 90% of their athletes have maintained a 4 year graduation rate. It is believed that the rate is lower than 90%. The hypotheses are: H0: p = 0.90 H1: p

Question

over the past ten years 90% of their athletes have maintained a 4 year graduation rate. It is believed that the rate is lower than 90%. The hypotheses are: H0: p = 0.90 H1: p < 0.90 where p is the unknown proportion of athletes that graduate within 4 years. A random sample of 65 athlete alumni from the past 10 years and decides to reject H0 if the sample proportion of ex-athletes who graduated within 4 years is less than or equal to 0.85. 
(a) What is the approximate distribution of the sample proportion p-hat if H0 is true? 
 (b) Based on the decision rule, what is the value of α, the probability of a Type I error? 
 (c) Suppose that 51 of the sampled athletes say that they graduated within 4 years. What is the p-value for this test? 
 (d) At the given level of significance (part b) what is the decision?