A simple random sample of 20 items resulted in a sample mean of 20. The population standard deviation is = 6. Round your answers to two decimal places. a. What is the standard error of the mean, o? b. At 95% confidence, what is the margin of error?
A simple random sample of 20 items resulted in a sample mean of 20. The population standard deviation is = 6. Round your answers to two decimal places. a. What is the standard error of the mean, o? b. At 95% confidence, what is the margin of error?
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 Calculation and Confidence Intervals**
A simple random sample of 20 items resulted in a sample mean of 20. The population standard deviation is \( \sigma = 6 \). Round your answers to two decimal places.
a. **What is the standard error of the mean, \( \sigma_{\bar{x}} \)?**
\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]
(Sample size \( n = 20 \))
b. **At 95% confidence, what is the margin of error?**
\[ \text{Margin of Error} = Z \times \sigma_{\bar{x}} \]
(For 95% confidence, \( Z \approx 1.96 \))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F375a8daa-a061-40df-aa13-f324a3b06fab%2Ff2f1cf1a-79fe-47d5-ba0c-352d5c7c5de4%2Fhosczpe_processed.png&w=3840&q=75)
Transcribed Image Text:**Sample Size Calculation and Confidence Intervals**
A simple random sample of 20 items resulted in a sample mean of 20. The population standard deviation is \( \sigma = 6 \). Round your answers to two decimal places.
a. **What is the standard error of the mean, \( \sigma_{\bar{x}} \)?**
\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]
(Sample size \( n = 20 \))
b. **At 95% confidence, what is the margin of error?**
\[ \text{Margin of Error} = Z \times \sigma_{\bar{x}} \]
(For 95% confidence, \( Z \approx 1.96 \))
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