0.43/0.75 Points] DETAILS PREVIOUS ANSWERS USEESTAT4 20.E.014.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A university is contemplating switching from the quarter system to the semester system. The administration conducts a survey of a random sample of 500 students and finds that 300 of them prefer to remain on the quarter system. USE SALT (a) Construct a 95% confidence interval for the true proportion of all students who would prefer to remain on the quarter system. (Round your answers to two decimal places.) (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. (Round your answer to the nearest percent, when necessary.) %, that the majority of students prefer to remain on the quarter We can be confident based on the 95% confidence interval, systems, since the interval entirely above 50% %to (c) Now suppose that only 30 students had been surveyed and that 18 said they preferred the quarter system. Compute a 95% confidence interval for the true proportion that prefers to remain on the quarter system. (Round your answers to two decimal places.) to Does the interval provide convincing evidence that the majority of students prefer to remain on the quarter system? (Round your answer to the nearest percent, when necessary) No We cannot be confident based on the 95% confidence interval, of systems, since the interval contains values above and below 50% %, that the majority of students prefer to remain on the quarter (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. The larger sample size in part (a) yielded a smaller standard error, and thus a smaller sample size produces a smaller 95% confidence interval. Need Help? confidence interval, than the smaller sample size in part (c). In general, a larger