A university is contemplating switching from the quarter system to the semester system. The administration conducts a survey of a random sample of 400 students and finds that 240 of them prefer to remain on the quarter system.
a. Construct a 95% confidence interval for the true proportion of all students who would prefer to remain on the quarter system.
b. Does the interval you computed in part (a) provide convincing evidence that the majority of students prefer to remain on the quarter system? Explain.
c. Now suppose that only 50 students had been surveyed and that 30 said they preferred the quarter system. Compute a 95% confidence interval for the true proportion that prefers to remain on the quarter system. Does the interval provide convincing evidence that the majority of students prefer to remain on the quarter system?
d. Compare the sample proportions and the con­fidence intervals found in parts (a) and (c). Use these results to discuss the role sample size plays in helping make decisions from sample data.