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Determine construct the sample size is 5 and the level confidence is 99.9%. the value of t necessary to a confidence interval when

Determine construct the sample size is 5 and the level confidence is 99.9%. the value of t necessary to a confidence interval when

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 3BGP
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**Constructing a Confidence Interval** To determine the value of \( t \) necessary for constructing a confidence interval when the sample size is 5 and the level of confidence is 99.9%, follow these steps: 1. **Determine Degrees of Freedom (df):** - Degrees of Freedom: \( df = n - 1 \) - Given sample size (\( n \)) is 5. - \( df = 5 - 1 = 4 \) 2. **Locate \( t \)-Value:** - Using a *t-distribution table* or statistical software, locate the \( t \)-value corresponding to \( df = 4 \) for a 99.9% confidence level. - For a 99.9% confidence level, the critical region is \( \alpha = 0.001 \), and hence, you look for \( \frac{\alpha}{2} = 0.0005 \). By consulting a t-distribution table or relevant software, you can find this specific \( t \)-value. Ensure your resources provide accurate \( t \)-values for high confidence levels and corresponding degrees of freedom. Understanding and applying the correct \( t \)-value is crucial in achieving accurate results in statistical analysis, ensuring the reliability of your confidence intervals.
Transcribed Image Text:**Constructing a Confidence Interval** To determine the value of \( t \) necessary for constructing a confidence interval when the sample size is 5 and the level of confidence is 99.9%, follow these steps: 1. **Determine Degrees of Freedom (df):** - Degrees of Freedom: \( df = n - 1 \) - Given sample size (\( n \)) is 5. - \( df = 5 - 1 = 4 \) 2. **Locate \( t \)-Value:** - Using a *t-distribution table* or statistical software, locate the \( t \)-value corresponding to \( df = 4 \) for a 99.9% confidence level. - For a 99.9% confidence level, the critical region is \( \alpha = 0.001 \), and hence, you look for \( \frac{\alpha}{2} = 0.0005 \). By consulting a t-distribution table or relevant software, you can find this specific \( t \)-value. Ensure your resources provide accurate \( t \)-values for high confidence levels and corresponding degrees of freedom. Understanding and applying the correct \( t \)-value is crucial in achieving accurate results in statistical analysis, ensuring the reliability of your confidence intervals.
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