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Use this information to answer the next four questions 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 2010 graduated within six years. In a random sample of 190 student athletes in this university, 137 graduated within six years. Is there sufficient evidence to believe that the proportion of athletes who graduate within six years is less than 78%? Use α-.05. 34. PLAN: Give the name of the correct procedure to use (2 points), the parameter of interest in the context of the problem (2 points), the null and alternative hypotheses (2 points), and the level of significance you will use (1 point).
35. SOLVE: List the conditions for the test you plan to use (2 points), explain how these conditions are met (2 points), calculate and write down the test statistic (3 points), and find the P-value (2 points).
36.CONCLUDE: Based on your P-value, conclude in context. (3 points)
37. Suppose that a 95% confidence interval estimate for the proportion of athletes who graduate within six years in this university was calculated to be (0.66, 0.78) Interpret this interval in context. (3 points)
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F14 fROUND( (B7-B2)/SORT (B2* B9/B3),P2) Question 34) Step 1 2 0.78 190 137 0.05 HO: The proportion of athlets who graduate within six years is not less than 78% 4 H: P 0.78 H1: The proportion of athlets who graduate within six years is less than 78% H P 0.78 0.7211Question 35) Step 2: np = 190*0.78 = 148.2 which is greater than 5 and nq 190*(1-0.78) There fore, normality conditions are satiesfied 0.22 41.8 which is also greater than 5 10 12 13 14 15 16 17 Step 3:Test statistic 1.9599 B7-B2)/SQRT(B2B9/B3) P-value 0.025 =NORM.S.DIST(F14,TRUE Step 4: Question 36) Step 5: 19 Here p-value alpha 0.05 reject Ho so we 21 Thus, we conclude that The proportion of athlets who graduate within six years is less than 78%

Question 37)

The 95% chance that the propotion of athletes who graduage within six years in this university is lies between 0.66 and 0.78 i.e. 66% to 78%

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