Assume that a sample is used to estimate a population proportion μ. Find the margin of error M.E. that corresponds to a sample of size 709 with a mean of 42.1 and a standard deviation of 17.5 at a confidence level of 90%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
Assume that a sample is used to estimate a population proportion μ. Find the margin of error M.E. that corresponds to a sample of size 709 with a mean of 42.1 and a standard deviation of 17.5 at a confidence level of 90%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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![### Estimating the Margin of Error for a Population Proportion
**Problem Statement:**
Assume that a sample is used to estimate a population proportion \( \mu \). Find the margin of error \( M.E. \) that corresponds to a sample of size 709 with a mean of 42.1 and a standard deviation of 17.5 at a confidence level of 90%.
**Instructions:**
Report the margin of error (M.E.) accurate to one decimal place because the sample statistics are presented with this accuracy.
\[ M.E. = \boxed{} \]
**Additional Notes:**
- Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
This exercise involves calculating the margin of error for the given sample statistics. The critical value for a 90% confidence level is generally 1.645 when using the z-distribution for large samples.
To find the margin of error, use the formula:
\[ M.E. = z \times \left( \frac{\sigma}{\sqrt{n}} \right) \]
Where:
- \( z \) is the critical value for the desired confidence level,
- \( \sigma \) is the standard deviation,
- \( n \) is the sample size.
### Example Calculation (Not part of the original problem statement)
For illustrative purposes, assume the critical value \( z \) for a 90% confidence interval is 1.645.
\[ M.E. = 1.645 \times \left( \frac{17.5}{\sqrt{709}} \right) \]
Perform the computation step-by-step to find the numerical value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd120f3b3-582e-4ce3-bf67-95261f57ecc8%2F96ce3655-6061-49a7-999b-d347e91186b3%2F0jvnu98_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Estimating the Margin of Error for a Population Proportion
**Problem Statement:**
Assume that a sample is used to estimate a population proportion \( \mu \). Find the margin of error \( M.E. \) that corresponds to a sample of size 709 with a mean of 42.1 and a standard deviation of 17.5 at a confidence level of 90%.
**Instructions:**
Report the margin of error (M.E.) accurate to one decimal place because the sample statistics are presented with this accuracy.
\[ M.E. = \boxed{} \]
**Additional Notes:**
- Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
This exercise involves calculating the margin of error for the given sample statistics. The critical value for a 90% confidence level is generally 1.645 when using the z-distribution for large samples.
To find the margin of error, use the formula:
\[ M.E. = z \times \left( \frac{\sigma}{\sqrt{n}} \right) \]
Where:
- \( z \) is the critical value for the desired confidence level,
- \( \sigma \) is the standard deviation,
- \( n \) is the sample size.
### Example Calculation (Not part of the original problem statement)
For illustrative purposes, assume the critical value \( z \) for a 90% confidence interval is 1.645.
\[ M.E. = 1.645 \times \left( \frac{17.5}{\sqrt{709}} \right) \]
Perform the computation step-by-step to find the numerical value.
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