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A hospital administrator wants to estimate the proportion of patients whose hospital stay exceeds a week. How many patients should be sampled to estimate the proportion staying more than a week to within 6 percentage points with 98% confidence?

A hospital administrator wants to estimate the proportion of patients whose hospital stay exceeds a week. How many patients should be sampled to estimate the proportion staying more than a week to within 6 percentage points with 98% confidence?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Sample Size Estimation for Hospital Stay Analysis** A hospital administrator wants to estimate the proportion of patients whose hospital stay exceeds a week. How many patients should be sampled to estimate the proportion staying more than a week to within 6 percentage points with 98% confidence? [Calculation required here] To determine the appropriate sample size, you can use the formula for the sample size of a proportion: \[ n = \left( \frac{Z^2 \times p \times (1-p)}{E^2} \right) \] Where: - \( n \) is the sample size - \( Z \) is the Z-value (from Z-table corresponding to the desired confidence level, 98% in this case) - \( p \) is the estimated proportion of patients staying more than a week (if unknown, use 0.5 for maximum variability) - \( E \) is the margin of error (6 percentage points = 0.06) Substitute the values into the formula to find the required sample size.
Transcribed Image Text:**Sample Size Estimation for Hospital Stay Analysis** A hospital administrator wants to estimate the proportion of patients whose hospital stay exceeds a week. How many patients should be sampled to estimate the proportion staying more than a week to within 6 percentage points with 98% confidence? [Calculation required here] To determine the appropriate sample size, you can use the formula for the sample size of a proportion: \[ n = \left( \frac{Z^2 \times p \times (1-p)}{E^2} \right) \] Where: - \( n \) is the sample size - \( Z \) is the Z-value (from Z-table corresponding to the desired confidence level, 98% in this case) - \( p \) is the estimated proportion of patients staying more than a week (if unknown, use 0.5 for maximum variability) - \( E \) is the margin of error (6 percentage points = 0.06) Substitute the values into the formula to find the required sample size.
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