4. A professor was curious as to whether the students in a very large class who turned in their tests first scored differently from the overall mean on the test. The overall mean score on the test was 75, with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 tests was 78. Was the mean test score for students who turned in their tests first significantly different from the overall mean at the .05 level? (6 marks) a) Use the five steps of hypothesis testing, making sure to calculate M and SDM. b) What is the shape of the comparison distribution? c) Calculate the confidence limits for the 95% confidence interval.