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Complete Question
As an aid to the establishment of personnel requirements, 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 = 396 and S = 100. Using the sample standard deviation as an estimate for the population standard deviation, what size sample should the director choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability, what size sample should she choose?
Answer:
Sample size n = 16
Explanation:
We use the formula for Margin of Error for the question
Margin of Error = z × Standard deviation/√n
Margin of Error = 1
z score for 99% confidence interval = 2.576
Standard deviation = 100
1 = 2.576 × 100/√n
1 × √n = 257.6
√n = 257.6/1
n = √257.6
n = 16.049922118
Approximately = 16
Therefore, the sample size = 16