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ind the necessary confidence interval for a population mean u for the following values. (Round your answers to three decimal places a 90% confidence interval, n = 135, x = 0.87, s? = 0.089 %3D

ind the necessary confidence interval for a population mean u for the following values. (Round your answers to three decimal places a 90% confidence interval, n = 135, x = 0.87, s? = 0.089 %3D

MATLAB: An Introduction with Applications
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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**Confidence Interval for a Population Mean** To find the necessary confidence interval for a population mean \( \mu \), use the following information: - **Confidence level**: 90% - **Sample size** (\( n \)): 135 - **Sample mean** (\( \bar{x} \)): 0.87 - **Sample variance** (\( s^2 \)): 0.089 **Steps to calculate the confidence interval:** 1. **Determine the standard deviation** (\( s \)): Take the square root of the variance. 2. **Find the standard error** (\( SE \)): Calculate it as \( \frac{s}{\sqrt{n}} \). 3. **Calculate the critical value**: Look up the z-score for a 90% confidence level (typically found in a z-table). 4. **Determine the margin of error** (\( ME \)): Multiply the critical value by the standard error. 5. **Compute the confidence interval**: Add and subtract the margin of error from the sample mean. **Example Attempts:** - Attempted lower limit: 0.857 - Attempted upper limit: 0.883 Note: These attempts were marked incorrect, suggesting a miscalculation or rounding error. Ensure calculations are rounded to three decimal places.
Transcribed Image Text:**Confidence Interval for a Population Mean** To find the necessary confidence interval for a population mean \( \mu \), use the following information: - **Confidence level**: 90% - **Sample size** (\( n \)): 135 - **Sample mean** (\( \bar{x} \)): 0.87 - **Sample variance** (\( s^2 \)): 0.089 **Steps to calculate the confidence interval:** 1. **Determine the standard deviation** (\( s \)): Take the square root of the variance. 2. **Find the standard error** (\( SE \)): Calculate it as \( \frac{s}{\sqrt{n}} \). 3. **Calculate the critical value**: Look up the z-score for a 90% confidence level (typically found in a z-table). 4. **Determine the margin of error** (\( ME \)): Multiply the critical value by the standard error. 5. **Compute the confidence interval**: Add and subtract the margin of error from the sample mean. **Example Attempts:** - Attempted lower limit: 0.857 - Attempted upper limit: 0.883 Note: These attempts were marked incorrect, suggesting a miscalculation or rounding error. Ensure calculations are rounded to three decimal places.
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