6. A professor of a statistics course surveyed her students to see how many of them were getting at least 8 hours of sleep per night. Only two of her 30 students were getting at least 8 hours of sleep

6. A professor of a statistics course surveyed her students to see how many of them were getting at least 8 hours of sleep per night. Only two of her 30 students were getting at least 8 hours of sleep per night.

(a) Treating the professor’s class as a random sample of all students at the instructor’s university, find a 95% confidence interval for the proportion of the entire student body that is getting at least 8 hours of sleep per night. Use the plus four confidence interval.