Answer to Question #175740 in Statistics and Probability for Ajay Singh

Question

1.      To decide what personnel requirements should be enforced, a hospital manager wants to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 48 different 24-hour periods and counts the number of admissions for each. In his sample, the sample mean is 396 and the sample standard deviation is 110. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval. (1)

 

2.      Using the sample standard deviation as an estimate for the population standard deviation, what size sample should the manager choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 98% reliability? (1)

 

Answer 1

1) $95\%CI=(396-1.96\frac{110}{\sqrt{48}},396+1.96\frac{110}{\sqrt{48}})=(364.059, 427.941).$

2) $n=(\frac{2.326*110}{1})^2=65465.$