Answer the question below.

8. (15 pt) From a survey of 400 elementary school teachers and 220 high school teachers, 240 of the elementary school teachers and 148 of the high school teachers said they were very satisfied with their jobs. Assume that the data represent two independent random samples. a. (8) At a level of significance of 0.05, does the data provide enough evidence that a higher proportion of high school teachers are satisfied with their jobs than elementary school teachers? Go through the 8 steps of hypothesis testing using rejection region. b. (5) Construct an appropriate confidence interval for the proportion of high school teachers who are satisfied with their jobs minus that of elementary school teachers and use this CI to argue why or why not you can conclude that the proportion of high school teachers who are satisfied with their jobs is higher than that of elementary school teachers at a 0.01 level of significance. c. (2) Are your conclusions in parts (a) and (b) consistent with each other? Why or why not