The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, $\bar { x } = 19.8$ and $s ^ { 2 } = 4$. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with $90 \%$ reliability, what is the minimum sample size she should use?
A) 7
B) 27
C) 44
D) 11

Question

Quizplus · Accepted Answer

The sample size needed to estimate the mean number of admissions per 24-hour period to within 1 admission with 90% reliability is given by:$$n = \frac{z^2 s^2}{e^2}$$where:* z is the z-score for the desired confidence level* s is the sample standard deviation* e is the margin of errorPlugging in the given values, we get:$$n = \frac{1.645^2 	imes 4}{1^2} = 27.06$$Rounding up to the nearest whole number, the minimum sample size the director should use is 27.

The Director of a Hospital Wishes to Estimate the Mean xˉ=19.8\bar { x } = 19.8xˉ=19.8

The Director of a Hospital Wishes to Estimate the Mean $\bar { x } = 19.8$