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, x = 19.8 and s2 = 36. 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)3508
B)60
C)98
D)2132

Question

Quizplus · Accepted Answer

The minimum sample size can be calculated using the formula for the sample size of a population mean: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the desired confidence level (90% in this case, which gives a Z-score of approximately 1.645), $\sigma$ is the standard deviation (the square root of $s^2$, which is 6), and $E$ is the margin of error (1 admission). Plugging in the values: $n = \left(\frac{1.645 \cdot 6}{1}\right)^2 = \left(9.87\right)^2 \approx 97.4$, which rounds up to 98 for a whole number of samples.

The Director of a Hospital Wishes to Estimate the Mean