Question

Question 7 3 pts 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 WN Mean Median Min Max Variance Std Deviation су Count Private 70.526 69.000 49.000 87.000 139.374 11.806 16.739 19 Public 57.294 61.000 32.000 86.000 197.346 14.048 24.519 17 Private Public STEM Leaf STEM Leaf 2 21 3278 4 9 44 5689 51129 6011789 61 245668 7 45 9 72 80244 77 86 9 A value of 419 is an rate of 49% A value of 32 is an rate of 32% 9 The standard Error for this problem, based on the assumption of equal variances, is 12.909 166.655 4.310 4.532

Answer 1

Sample variances are  

si = 139.374 and s 197.346

Sample sizes are

$Pooled\ variance \ s_p^2 = \frac{(n_1-1)*s_1^2 \ +\ (n_2-1)*s_2^2 }{n_1+n_2-2} \\ \ \\ = \frac{(19-1)*139.374 + (17-1)*197.346}{19+17-2} \\ \ \\ = 166.6549$

$Standard \ Error\ (SE)\ = \sqrt{s_p^2*(\frac{1}{n_1} + \frac{1}{n_2})} \\ \ \\ = \sqrt{166.6549*(\frac{1}{19} + \frac{1}{17})} \\ \ \\ =\sqrt{166.6549*0.1114551} \\ \ \\ = 4.310$

Therefore, standard error is option (C) 4.310