The University of MissouriSt.Louis gave a validation test to entering students who had taken calculus in high school. There are 121 students overall, 28 of which received college credit for the calculus they took in high school and 93 of which did not receive college credit. The group of 93 students receiving no college credit had a mean score of 4.17 on the validation test with a sample standard deviation of 3.7 (s = V208,- X)2/ (93 1) = 3.7). For the 28 students who received credit from a high school dualenrollment class, the mean score was 4.61 with a sample standard deviation of 4.28. (a) Find a 95% condence interval of the true mean for students not receiving college credit. (b) Find a 95% condence interval of the true mean for students receiving college credit. (0) Find a 95% condence interval for. the difference in the means between the two groups. To construct this condence interval, use a tdistribution with 40 degrees of freedom. See the degrees of freedom approximation below: 2 a} 2 o 2 . 2 4'2 2 2 2 df % (323/91, +so) = (3 72/932+ 82/ 82 m 39.92 (s.,)2 (32mg)? (3.7 /93) (4.28 /28) nil + nol 92 + 27 (d) Test the null hypothesis that there is no difference in true means between the two populations based on the samples you have observed