Hypotheses testing suppose we know that changes in score follow a normal distribution

3. Consider Exercise 3 from Section 9.2. Here are the changes in score for 46 randomly chosen high school students: -30 24 47 70 -62 55 -41 -32 128 -11 -43 122 -10 56 32 -30 -28 -19 1 17 57-14-58 77 27-33 51 17-67 29 94 -11 2 12-53 -49 49 8 -24 96 120 2-33 -2-39 99 Suppose we know that changes in score follow a normal distribution with standard deviation o = 50. [2, 14.18] (a) Find the p-value for the result from the obtained data AND say if you used the z-distribution or the t-distribution. (b) Are the results significant at the a = 0.05 level? (c) What do you do with the null hypothesis Ho? (d) Using complete sentences, state the "real-world" conclusion about changes in students' SAT math scores