Problem3 (Use the Formula sheet and the Tables to answer this question, You should not use Mega-Stat) A sample of 10 students were given a diagnostic test before studying a particular module and then again after completing the module. The scores before studying the module and after studying the module are used to find this Mega-Stat output: Descriptive statistics Difference After- Before count 10 mean 1.60 sample variance 8.71 sample standard deviation. 2.95 minimum maximum range 875459 -4 normal curve GOF p-value chi-square(df-1) .1573 2.00 E 2.50 O(-0.67) O(+0.00) O(+0.67) O(inf.) 288243 1 Hypothesis Test: Paired Observations 0.000 hypothesized value 21.500 mean After- test score 19.900 mean Before-test score mean difference (After- test score - Before-test 1.600 score) 2.951 std. dev. 0.933 std. error 10 Π 9 df t Mailings Review View Grammarly Tell me ↓ ་་ AaBbCcDUER ABBCCOVER |AaBbCcDdl Aal Normal No Spacing Heading 1 H v mean difference (After- test score Before-test 1.600 score) 2.951 std. dev. 0.933 std. error 10 n 9 df 0603 p-value (one-tailed, upper) 2.111 confidence interval 95% lower confidence interval 95.% upper margin of error Use the above output to solve the following questions: (a) Write the null Ho and alternative hypotheses HI a) Test normality of the deference between the scores after studying the module and before studying the module b) Calculate the test statistic T c) Use the p-value to test the hypothesis: Is there evidence that the module improved the scores at a -0.057 a) Construct a 95% confidence interval for the difference between the means of the pre-test scores and the post-test scores. Fo