Question

A university wants to evaluate its graduation rates to comply with NCAA regulations. The "Student Success Management" division determines that if the school wants to meet current NCAA standards, it will have to have at least an 86% graduation rate among its student athletes who qualify under the NCAA definitions of a "graduating student athlete." The athletic department will take corrective actions if the graduation rate of those student athletes falls below 86%. A survey of 1,400 student athletes in all sports offered at the university show that 1,176 graduated with a certificate or degree from the university. Use Table 1.

a.

Select the hypotheses to test if the university needs to improve its graduation rate.

	H0: p = 0.86; HA: p ? 0.86
	H0: p ? 0.86; HA: p < 0.86
	H0: p ? 0.86; HA: p > 0.86

b.	What is the value of the test statistic? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Test statistic

c.	Compute the p-value. (Round "z-value" to 2 decimal places and final answer to 4 decimal places.)

p-value

d.

At ? = 0.05, what is the conclusion?

	The management will not take corrective action
	The management will take corrective action

Answer 1

a) HO: P > 0.86

   HA: P < 0.86

b) p = 1176/1400 = 0.84

The test statistic z = (p - P)/sqrt(P(1 - P)/n)

                             = (0.84 - 0.86)/sqrt(0.86 * (1 - 0.86)/1400)

                             = -2.16

c) P-value = P(Z < -2.16)

                = 0.0154

d) As the P-value is less than the significance level (0.0154 < 0.05), we should reject H₀.

So at alpha = 0.05, we can conclude that the management will take corrective action.