proportion of males among patients discharged from Pennsylvania follows: Is the number (1.96) If not, how do you get it? Thank you! Please explain! a constant?
proportion of males among patients discharged from Pennsylvania follows: Is the number (1.96) If not, how do you get it? Thank you! Please explain! a constant?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Chapter 6, Problem 17P**
**Objective:**
To determine the 95% confidence interval for the percentage of males among patients discharged from Pennsylvania hospitals.
---
**Solution and Explanation:**
**Answer to Problem 17P:**
The 95% confidence interval for the percentage of males among patients discharged from Pennsylvania hospitals is (0.25, 0.63).
**Explanation of Solution:**
1. From Exercise 15, the best point estimate for the percentage of males among patients discharged from Pennsylvania hospitals, \( \hat{p} \), is 0.44.
2. From Exercise 15, the standard error of the sample proportion is 0.099.
3. Since the required confidence interval is 95%, the two-tailed z-critical value is 1.96.
4. The 95% confidence interval for the proportion of males among patients discharged from Pennsylvania hospitals is calculated as follows:
\[
CI = \hat{p} \pm z_{\alpha/2} (SE)
\]
\[
= 0.44 \pm (1.96)(0.099)
\]
\[
= 0.44 \pm 0.19404
\]
\[
= (0.24596, 0.63404) \approx (0.25, 0.63)
\]
Thus, the 95% confidence interval for the percentage of males among patients discharged from Pennsylvania hospitals is (0.25, 0.63).
*Note: A handwritten note asks: "Is the number (1.96) a constant? If not, how do you get it? Thank you! Please explain!" This refers to the z-critical value, which is a constant for a 95% confidence interval.*
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Transcribed Image Text:**Chapter 6, Problem 17P**
**Objective:**
To determine the 95% confidence interval for the percentage of males among patients discharged from Pennsylvania hospitals.
---
**Solution and Explanation:**
**Answer to Problem 17P:**
The 95% confidence interval for the percentage of males among patients discharged from Pennsylvania hospitals is (0.25, 0.63).
**Explanation of Solution:**
1. From Exercise 15, the best point estimate for the percentage of males among patients discharged from Pennsylvania hospitals, \( \hat{p} \), is 0.44.
2. From Exercise 15, the standard error of the sample proportion is 0.099.
3. Since the required confidence interval is 95%, the two-tailed z-critical value is 1.96.
4. The 95% confidence interval for the proportion of males among patients discharged from Pennsylvania hospitals is calculated as follows:
\[
CI = \hat{p} \pm z_{\alpha/2} (SE)
\]
\[
= 0.44 \pm (1.96)(0.099)
\]
\[
= 0.44 \pm 0.19404
\]
\[
= (0.24596, 0.63404) \approx (0.25, 0.63)
\]
Thus, the 95% confidence interval for the percentage of males among patients discharged from Pennsylvania hospitals is (0.25, 0.63).
*Note: A handwritten note asks: "Is the number (1.96) a constant? If not, how do you get it? Thank you! Please explain!" This refers to the z-critical value, which is a constant for a 95% confidence interval.*
---
Expert Solution
Step 1
Given that
Confidence Level = 95%
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