Determine the sample size required to estimate a population mean to within 8 units given that the population standard deviation is 55. Use a confidence level of 95%. Sample Size = 0
Determine the sample size required to estimate a population mean to within 8 units given that the population standard deviation is 55. Use a confidence level of 95%. Sample Size = 0
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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Question
![**Determine the Sample Size Required**
To estimate a population mean within 8 units, given the following parameters:
- **Population Standard Deviation**: 55
- **Confidence Level**: 95%
Calculate the sample size needed.
**Formula**:
The sample size (n) can be calculated using the following formula:
\[ n = \left( \frac{Z \times \sigma}{E} \right)^2 \]
Where:
- \( Z \) is the Z-value (Z-score) corresponding to the desired confidence level (for 95%, \( Z \approx 1.96 \))
- \( \sigma \) is the population standard deviation (55)
- \( E \) is the margin of error (8)
**Sample Size =** [Box for input]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20960b1b-ef33-4f67-8b23-d0d3dcfa80e2%2F86d316f7-6aaa-4b2a-9f1c-2e8b2f80350b%2Fr9crlcl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine the Sample Size Required**
To estimate a population mean within 8 units, given the following parameters:
- **Population Standard Deviation**: 55
- **Confidence Level**: 95%
Calculate the sample size needed.
**Formula**:
The sample size (n) can be calculated using the following formula:
\[ n = \left( \frac{Z \times \sigma}{E} \right)^2 \]
Where:
- \( Z \) is the Z-value (Z-score) corresponding to the desired confidence level (for 95%, \( Z \approx 1.96 \))
- \( \sigma \) is the population standard deviation (55)
- \( E \) is the margin of error (8)
**Sample Size =** [Box for input]
Expert Solution
Step 1: Information given is
Margin of error(E)=8
standard deviation(
)=55
confidence level=95%
Step by step
Solved in 3 steps with 6 images
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