Question

QUESTION 39 {Narrative: Graduate) 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: 45 of the 74 athletes admitted in a specific year graduated within 6 years. Does the proportion of athletes who graduate di ffer significantly from the all-university proportion, which is .70 ? What is the sample size O45 0 74 O 119 O 0.029

Answer 1

Solution: Given data: Sample Size (n)= 74 X= 4.5 number of athletes admitted in a specific year Graduated with 6 years. Ans (39) Sample Size (n) = 74 Ane (40) Sample proportion Х - 0.61 45 74 n þ= 0.61 Aus (41) Null and Alteenative Hypothesis Null (Ho): P= 0.70 Alternative (Hi): P is not 0.70 This is two tailed test. 142 Test statistic Undes Ho Ane 1 Z = þ-P poln

where P=0.70 Q=1-P 1-0.70 = 0.30 0.61 -0.70 ze -0.09 0.0028 OoFox 0.30 74 IZ cle 70 -0.09 0.0529 Z= -1,70 Ans (UB) normal P-value is determined using tables. for two tailed test P-value is 0.0446 010446 - 1.70 +1.70 P-value=P(Z<-1.70) + P(Z > 1170) 0.0446 + 0.0446 0.0892 I using P value = 0.0892 - normal tables

conclusion: Since the p-value (0.0892) >0.05, we failed to reject the null Hypothesis. This means that the sample evidence is not Strong enough to conclude that the proportion of athletes who graduate differes significantly from the all-university proportion of 0.7o. Ans 46) Power of test = 87% I-B 87% - - 0 B B 1 87% -0.87 0:13 B = type ll error probabilily B = 0.13 13% B = 13%