(F). (Round to three decimal places as Evaluate the formula E=z, # where z = 1.960, o= 32.43, and n = 45. *** needed.)
(F). (Round to three decimal places as Evaluate the formula E=z, # where z = 1.960, o= 32.43, and n = 45. *** needed.)
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
Q5
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**Evaluating the Margin of Error in Statistical Analysis**
In statistics, the margin of error (E) is a measure of the expected variability of a sample estimate from the true population parameter. It is calculated using the formula:
\[ E = z \times \left( \frac{\sigma}{\sqrt{n}} \right) \]
Where:
- \( z \) is the z-score corresponding to the desired confidence level.
- \( \sigma \) (sigma) is the standard deviation of the population.
- \( n \) is the sample size.
Given the following values:
\[ z = 1.960, \sigma = 32.43, \text{ and } n = 45 \]
We can substitute these values into the formula to find the margin of error.
Substitute the values into the formula:
\[ E = 1.960 \times \left( \frac{32.43}{\sqrt{45}} \right) \]
1. Calculate the square root of the sample size (n):
\[ \sqrt{45} \approx 6.708 \]
2. Divide the standard deviation (\(\sigma\)) by the square root of the sample size (\( \sqrt{n} \)):
\[ \frac{32.43}{6.708} \approx 4.835 \]
3. Multiply the result by the z-score:
\[ E = 1.960 \times 4.835 \approx 9.470 \]
Therefore, the margin of error \( E \) is:
\[ E \approx 9.470 \]
(Rounded to three decimal places as needed.)
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Transcribed Image Text:---
**Evaluating the Margin of Error in Statistical Analysis**
In statistics, the margin of error (E) is a measure of the expected variability of a sample estimate from the true population parameter. It is calculated using the formula:
\[ E = z \times \left( \frac{\sigma}{\sqrt{n}} \right) \]
Where:
- \( z \) is the z-score corresponding to the desired confidence level.
- \( \sigma \) (sigma) is the standard deviation of the population.
- \( n \) is the sample size.
Given the following values:
\[ z = 1.960, \sigma = 32.43, \text{ and } n = 45 \]
We can substitute these values into the formula to find the margin of error.
Substitute the values into the formula:
\[ E = 1.960 \times \left( \frac{32.43}{\sqrt{45}} \right) \]
1. Calculate the square root of the sample size (n):
\[ \sqrt{45} \approx 6.708 \]
2. Divide the standard deviation (\(\sigma\)) by the square root of the sample size (\( \sqrt{n} \)):
\[ \frac{32.43}{6.708} \approx 4.835 \]
3. Multiply the result by the z-score:
\[ E = 1.960 \times 4.835 \approx 9.470 \]
Therefore, the margin of error \( E \) is:
\[ E \approx 9.470 \]
(Rounded to three decimal places as needed.)
---
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