The National Collegiate Athletic Association NCAA requires c

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. Ninety-five of the 147 athletes admitted in 1989-1991 graduated within six years. Does this indicate at a 1% significance level that the proportion of athletes who graduate differ significantly from the all-university proportion, which was 70%?

Step 1: H0:    HA:

Step 2: z =

Step 3: p-value =

Step 4: Reject/accpet H0 ........

Solution

Step 1: H0: p=0.5

HA: p not equal to 0.5

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Step 2: z = (phat-p)/sqrt(p*(1-p)/n)

=(0.95-0.7)/sqrt(0.7*0.3/147)

=6.61

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Step 3: p-value = 2*P(Z>6.61) =0 (from standard normal table)

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Step 4: Reject/accpet H0 .....

Reject Ho.