Suppose you want to study the population of full-time college students in State X. In this state, there are 200,000 full-time college students. Out of these students,50,000 students study at private schools, and the other 150,000 students study at state schools. You have drawn a stratified sample using private school students and state school students as the two strata. For each student selected, you recorded how much money the student spent on tuition and other college expenses (expense) in 2009. The results are as follows:
Private School Students: n1 = 100, X1 = 30,000, s1 = 10,000.
State School Students: n2 = 200, X2 = 15,000, s2 = 4000.
(a) Let μ1 denote the mean "expense" of a private school student in State X in 2009. At a 95% level of confidence, test the null hypothesis that μ1 did not exceed $25,000.
(b) At a 95% level of confidence, test the null hypothesis that on the average, the expense by a private school student in 2009 did not exceed the expense by a state school student by more than $12,000.
This solution provides assistance with testing the null hypothesis for the example problem given.