n = 5,000 USE SALT Consider that for p = 0.6 and sample sizes of n = 30, n = 100, and n = 400 the margins of error are 0.175, 0.096, and 0.048 respectively. Comment on how an increased sample size affects the margin of error. O As the sample size increases the margin of error remains relatively constant. O As the sample size increases the margin of error decreases. O As the sample size increases the margin of error also increases.
n = 5,000 USE SALT Consider that for p = 0.6 and sample sizes of n = 30, n = 100, and n = 400 the margins of error are 0.175, 0.096, and 0.048 respectively. Comment on how an increased sample size affects the margin of error. O As the sample size increases the margin of error remains relatively constant. O As the sample size increases the margin of error decreases. O As the sample size increases the margin of error also increases.
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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![**Calculate the 95% Margin of Error for a Binomial Proportion**
To estimate a binomial proportion \( p \) for the sample size:
- \( n = 5,000 \)
Use \(\hat{p} = 0.6\) to calculate the standard error of the estimator. (Round your answer to three decimal places.)
**Interactive Tool:** [USE SALT]
---
**Analysis of Sample Size and Margin of Error**
Consider \(\hat{p} = 0.6\) with the following sample sizes and their margins of error:
- \( n = 30\), margin of error = 0.175
- \( n = 100\), margin of error = 0.096
- \( n = 400\), margin of error = 0.048
**Question:** Comment on how an increased sample size affects the margin of error.
- As the sample size increases, the margin of error remains relatively constant.
- As the sample size increases, the margin of error decreases.
- As the sample size increases, the margin of error also increases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbff43673-f06b-43ca-b409-46eb420ace6b%2Fce83dc1b-b7e1-45aa-8b67-d65ead0c4b52%2F2vri83_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculate the 95% Margin of Error for a Binomial Proportion**
To estimate a binomial proportion \( p \) for the sample size:
- \( n = 5,000 \)
Use \(\hat{p} = 0.6\) to calculate the standard error of the estimator. (Round your answer to three decimal places.)
**Interactive Tool:** [USE SALT]
---
**Analysis of Sample Size and Margin of Error**
Consider \(\hat{p} = 0.6\) with the following sample sizes and their margins of error:
- \( n = 30\), margin of error = 0.175
- \( n = 100\), margin of error = 0.096
- \( n = 400\), margin of error = 0.048
**Question:** Comment on how an increased sample size affects the margin of error.
- As the sample size increases, the margin of error remains relatively constant.
- As the sample size increases, the margin of error decreases.
- As the sample size increases, the margin of error also increases.
Expert Solution
Step 1
Given that
p^ = 0.6 , n1 = 30 , n2 = 100 , n3 = 400 , E1 = 0.175
E2 = 0.096 , E3 = 0.048
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