A doctor wants to estimate the mean length of hospital stay of covid-19 patients with a 98% confidence interval. Estimate the sample size required so that margin of error does not exceed 2 days. Assume population standard deviation o 6 days.
A doctor wants to estimate the mean length of hospital stay of covid-19 patients with a 98% confidence interval. Estimate the sample size required so that margin of error does not exceed 2 days. Assume population standard deviation o 6 days.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![**Problem Statement: Estimating Sample Size for Hospital Stay Analysis**
A doctor aims to determine the average length of hospital stay for COVID-19 patients, ensuring a 98% confidence level in the results. The goal is to figure out the necessary sample size so that the margin of error does not exceed 2 days. The standard deviation of the population is assumed to be \( \sigma = 6 \) days.
**Solution Approach:**
To solve this problem, you will need to use the formula for determining the sample size \( n \) for estimating a mean with a given margin of error \( E \):
\[
n = \left( \frac{Z \cdot \sigma}{E} \right)^2
\]
Where:
- \( Z \) is the Z-value corresponding to the desired confidence level (98% confidence level).
- \( \sigma \) is the population standard deviation (6 days).
- \( E \) is the margin of error (2 days).
**Steps:**
1. Determine the Z-value for a 98% confidence interval.
2. Substitute the values into the formula to calculate \( n \).
By following these steps, you will compute the appropriate sample size required to estimate the mean hospital stay length accurately within the specified margin of error.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27df1f94-faef-4ac2-91fa-8218e7ddf856%2F6ff40ee2-8bab-4ee1-bb45-3399951aee91%2Fj1ps4ht_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Estimating Sample Size for Hospital Stay Analysis**
A doctor aims to determine the average length of hospital stay for COVID-19 patients, ensuring a 98% confidence level in the results. The goal is to figure out the necessary sample size so that the margin of error does not exceed 2 days. The standard deviation of the population is assumed to be \( \sigma = 6 \) days.
**Solution Approach:**
To solve this problem, you will need to use the formula for determining the sample size \( n \) for estimating a mean with a given margin of error \( E \):
\[
n = \left( \frac{Z \cdot \sigma}{E} \right)^2
\]
Where:
- \( Z \) is the Z-value corresponding to the desired confidence level (98% confidence level).
- \( \sigma \) is the population standard deviation (6 days).
- \( E \) is the margin of error (2 days).
**Steps:**
1. Determine the Z-value for a 98% confidence interval.
2. Substitute the values into the formula to calculate \( n \).
By following these steps, you will compute the appropriate sample size required to estimate the mean hospital stay length accurately within the specified margin of error.
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