Question

Small Sample Difference of Means Test. Each year Forbes puts out data on the top college and universities in the U.S. The following is a sample from the top 300 institutions in 2015. The test we will look at is the difference in the average 4-year graduation rates of private and public schools. The data are given below. We can assume equal variances. Note: I used the variances for all my calculations. 4-year graduation rates by Public and Private status of Top Universities Private STEM Public STEM Leaf Leaf 3278 Mean Median Min Max Variance Std Deviation Private 70.526 69.000 49.000 87.000 139.374 11.806 16.739 Public 57.294 61.000 32.000 86.000 197.346 14.048 24.519 17 49 44 5 1 129 6 1 245668 5689 6011789 7 459 80 24477 су 712 Count 19 86 A value of 49 is an rate of 49% A value of 32 is an rate of 32% If a priori we thought private schools should have a higher 4-year average graduation rate than public schools, the conclusion of the hypothesis test for this problem would be to reject the null hypothesis at alpha = .01. O True O False

Answer 1

Answer: TRUE

Suftix I denotes for Suftix 2 denotes for Hoi Mi = 42 Private Publie vs Schools Schools Hai M,>l2 ni=19, n2 =17 Ti = 70.526, X2 = 57.294 si = 139.374, SŽ = 197.34 6 Xi - X2 Test Statistie, te 70.526 – 57.294 1 139.374 197.346 19 17 = 3.0401 19+17-2 degrees of freedom = nith2-2 = = 34. p-value = P( 534 >3.0401) = 0.0023 ** since the p-value is less than the alpha level of 0.01, we reject the hull hypothenis.