In your STOR 155 class, the professor returns Midterm 2 and claims that the average score was 83 out of 100 with a standard deviation of 8 points. When the professor steps out of the room, you quickly select a simple random sample of students (all students are present that day) and note their scores: 68, 75, 74, 78, 75, 79, 65, 77, 85, 71 ) You strongly suspect that the professor is overstating the average so that students will blame themselves if they have a low Midterm score. State the null and alternative hypotheses for the appropriate test of significance at a=0.05. O Ho: M = 83; Ha: M # 83 O Ho: M = 83; Ha: M > 83 O Ho: M 83; Ha: M = 83 b) Find the z -statistic and P-value for these data. Give z to two decimal places and P to four decimal places. Z = and P = ) What is the appropriate decision based on P? Select all that apply. O We should fail to reject the null hypothesis in favor of the alternative hypothesis. O We should reject the null hypothesis in favor of the alternative. O We can say with certainty that the null hypothesis is not true