Question

1) Male athletes at Eastern Michigan University have a graduation rate of 71%. Over the past several years, a random sample of 42 male athletes at EMU showed that 24 eventually graduate. Does this indicate the population proportion of male athletes who graduate from EMU is now less than 71%? Use a 1% level of significance.

Step One: State the Hypotheses

Step Two: Calculate the Test Statistic

Step Three: Find the P-value

Step Four: Decision (compare the p-value to alpha)

Step Five: Conclusion (be sure this is in complete sentence form)

Answer 1

Step 1) null and alternative hypotheses

Ho : p = 0.71 Vs H1 : p < 0.71

Step 2) test statistic

Z = ( p^ - p)/sqrt [ p*(1-p)/n]

Where p^ = 24/42 = 0.57

Z = (0.57 - 0.71)/SQRT [ 0.71*9.29/42[

Z = -2.00

Step 3) p-value for Z = -2.00 and left tailed test

p-value = P( Z < -2.00)

p-value = 0.0228

Step 4) Here p-value = 0.0228 > 0.01

We fail to reject the null hypothesis Ho

Step 5) conclusion : There is no sufficient evidence to support the claim that the population proportion of male athletes who graduate from EMU is now less than 71%