c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical values. (3 Points) d. Decide whether to reject or fail to reject the null. ( 2 points) e. Make an interpretation of your decision in the context. ( 2 points)write your claim. (2 Points) b. Find the test statistic (3 Points) [Use Algebra first then Tech next] c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical values. (3 Points)The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers? Use a = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal. Teacher 1 Teacher 2 x1 = 473 x2 = 459 S1 = 39.7 S2 = 24.5 n 1 =8 n 2 = 18 a. State the null and alternate hypotheses (write it mathematically) and write your claim. (2 Points)