A hospital administrator wants to estimate the mean length of stay for all inpatients in that hos- pital. Based on a systematic random sample of 100 records of patients for the previous year, she reports that "The sample mean was 5.3. In repeated random samples of this size, the sample mean could be expected to fall within 1.0 of the true mean about 95% of the time."

(a) Construct and interpret a 95% confidence interval for the mean.

(b) The administrator decides that this interval is too wide, and she prefers one of only half this width. How large a sample size is needed?