Question

1. New York wants to do a study to compare students at two different schools in the city to see if student’s feelings about college are influenced by their tuition. The city takes a sample of 100 students from Barnard college whose tuition is 60 thousand dollars a year and 200 from Lehman College whose tuition is 15 thousand dollars a year. They ask each student the same question “Do you feel that your college is worth the tuition you pay for it?”. The survey found that 80% of the students at Lehman college agreed with the statement, while only 60% of the students at Barnard college agreed with the statement. The Research group believes that the proportion of students who agrees with the question will be the same between the two group. Assume that the data is normally distributed, and the sample was randomly selected. Please test this hypothesis and use an alpha of .05 for this study. Please answer the questions below. (points 10)
   1. What I the null and alternative hypotheses of the study? (2)
   2. What are the requirements for using a normal distribution to solve this problem? List them below (3)
   3. What is the critical value for this distribution? (1)
   4. What is the pooled probability of success for the study? (1)
   5. What is the sample statistics for this distribution? (1)
   6. Do I reject or accept the null hypotheses in my example? Explain? (1)

Answer 1

Here we will use z distribution to test the hypothesis because the population is normally distributed from which sample is taken.