4. In the past, the mean score of the seniors at South High on the American College Testing (ACT) college entrance examination has been 20. This year a special preparation course is offered, and all 53 seniors planning to take the ACT test enroll in the course. The mean of their 53 ACT scores is 22.1. The principal believes that the new course has improved the students' ACT scores. a) Assume that ACT scores vary normally with standard deviation 6. Is the outcome rat-bar = 22.1 good evidence that the population mean score is greater than 20? State and , compute the test statistic and the P-value, and answer the question by interpreting your result. b) The results are in any case inconclusive because of the design of the study. The effects of the new course are confounded with any change from past years, such as other new courses or higher standards. Briey outline the design of a better study of the effect of the new course on ACT scores