A new SAT study course is tested on 12 individuals. Pre-course and post-course scores are recorded. The following data is collected: Pre-course score Post-course score 960 920 1010 1100 840 880 1100 1070 1250 1320 860 860 1330 1370 790 770 990 1040 1110 1200 840 850 1200 1300 a) State the null and alternative hypotheses in terms of the appropriate parameter to test the claim that the study course improves students' SAT scores. (Use diff = post - pre.) Họ: ud points HA: ud points b) The level of significance is a = .05 (Hint: The level of significance is the p-value cutoff between rejecting or failing to reject the null hypothesis.) c) The test statistic is T V = 2.36 Use 33.33 for the mean and 49.05 for the standard deviation. d) The p-value is .03781 V. (If necessary, round your answer to four decimal places.) e) The correct decision is to reject the null hypothesis. f) There is sufficient evidence that the average score increased after taking the SAT study course. g) We are 95% confident that the average score improved between and points. (Use the e t Distribution Handout 7 (+] to find the confidence coefficient.)