A major hospital in Newfoundland is dealing with complaints that some nurses feel their schedules are worse than they were last year. A survey of 75 randomly selected nurses found an average satisfaction score of 6.5 for scheduling (on a scale of 1 to 10) with a standard deviation of 2.6, compared to an average score last year for all nurses of 7.1.

a) Calculate a 99% confidence interval for the survey result.

b) What can you say from this confidence interval about whether the score is different from last year?

c) If you wanted the confidence interval to have a width of 1, how many nurses should you survey?