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Find the critical value, for a 90% confidence when the sample size is 22.

Find the critical value, for a 90% confidence when the sample size is 22.

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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**Finding the Critical Value for a 90% Confidence Interval** To find the critical value for a 90% confidence level with a sample size of 22, follow these steps: 1. **Determine the Degrees of Freedom (df):** - The degrees of freedom is calculated as the sample size minus 1: \( df = 22 - 1 = 21 \). 2. **Select the Appropriate Distribution:** - Since the sample size is relatively small (less than 30), use the t-distribution. 3. **Find the Critical Value:** - Look up the critical value for a 90% confidence level and 21 degrees of freedom in a t-distribution table, or use statistical software. This value, denoted as \( t_{0.05} \) (since 5% is in each tail), is typically around 1.721. The critical value helps in constructing the confidence interval around a sample mean to estimate the population mean. For a deeper understanding, refer to statistical tables or use technology like calculators or computer software to find the exact critical value for \( t \).
Transcribed Image Text:**Finding the Critical Value for a 90% Confidence Interval** To find the critical value for a 90% confidence level with a sample size of 22, follow these steps: 1. **Determine the Degrees of Freedom (df):** - The degrees of freedom is calculated as the sample size minus 1: \( df = 22 - 1 = 21 \). 2. **Select the Appropriate Distribution:** - Since the sample size is relatively small (less than 30), use the t-distribution. 3. **Find the Critical Value:** - Look up the critical value for a 90% confidence level and 21 degrees of freedom in a t-distribution table, or use statistical software. This value, denoted as \( t_{0.05} \) (since 5% is in each tail), is typically around 1.721. The critical value helps in constructing the confidence interval around a sample mean to estimate the population mean. For a deeper understanding, refer to statistical tables or use technology like calculators or computer software to find the exact critical value for \( t \).
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