Do teachers find their work rewarding and satisfying? The results of a survey of random samples of 456 elementary school teachers and 345 high school teachers. Of the elementary teachers, 391 said they were very satisfied whereas 226 of the high school teachers said they were very satisfied. Based on this data is it reasonable to conclude that the proportion of very satisfied teachers is different for elementary school teachers that it is for high school teachers.  Let a = 0.05

An instructor for a SAT prep course claims that the course will improve the test scores of students. The table shows the critical reading scores for 10 students the first two times they took the SAT. However before taking the test the second time, the students took a course to improve their critical reading scores. With α = 0.05, is there enough evidence to support the instructor's claim? Does your answer change if α = 0.01? Why or why not? 

Student          1,       2,      3,     4,    5,      6,     7,    8,     9,    10

Score (1st)     300, 450, 350, 430, 300, 470, 420, 370, 320, 410

Score (2nd)    400, 520, 400, 490, 340, 580, 450, 400, 390, 450