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Find the t values that form the boundaries of the critical region for a two-tailed test with a = .05 and sample size n = 6. +2.571 +3.571 ±2.170

Find the t values that form the boundaries of the critical region for a two-tailed test with a = .05 and sample size n = 6. +2.571 +3.571 ±2.170

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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If you calculate \( r^2 \) and get 0.25, this should be interpreted as a _______ effect. - Small - Medium - Large - Ginormous
Transcribed Image Text:If you calculate \( r^2 \) and get 0.25, this should be interpreted as a _______ effect. - Small - Medium - Large - Ginormous
**Problem Statement:** Find the \( t \) values that form the boundaries of the critical region for a two-tailed test with \( \alpha = 0.05 \) and sample size \( n = 6 \). **Options:** - \( \pm 2.571 \) - \( \pm 3.571 \) - \( \pm 2.170 \) - \( 0 \) **Explanation:** In hypothesis testing, the critical region is the area in the tails of the distribution where the test statistic would lead us to reject the null hypothesis. For a two-tailed test with significance level \( \alpha = 0.05 \), the critical region is split equally between the two tails of the distribution. The sample size \( n = 6 \) means we have \( n - 1 = 5 \) degrees of freedom. To find the critical \( t \) values, one would typically refer to a \( t \)-distribution table or use statistical software to find the values that correspond to a cumulative probability of \( 0.025 \) in each tail (i.e., the 97.5th percentile for the positive boundary and the 2.5th percentile for the negative boundary). These critical values determine where the actual sample mean would need to fall for the null hypothesis to be rejected at the 0.05 level of significance.
Transcribed Image Text:**Problem Statement:** Find the \( t \) values that form the boundaries of the critical region for a two-tailed test with \( \alpha = 0.05 \) and sample size \( n = 6 \). **Options:** - \( \pm 2.571 \) - \( \pm 3.571 \) - \( \pm 2.170 \) - \( 0 \) **Explanation:** In hypothesis testing, the critical region is the area in the tails of the distribution where the test statistic would lead us to reject the null hypothesis. For a two-tailed test with significance level \( \alpha = 0.05 \), the critical region is split equally between the two tails of the distribution. The sample size \( n = 6 \) means we have \( n - 1 = 5 \) degrees of freedom. To find the critical \( t \) values, one would typically refer to a \( t \)-distribution table or use statistical software to find the values that correspond to a cumulative probability of \( 0.025 \) in each tail (i.e., the 97.5th percentile for the positive boundary and the 2.5th percentile for the negative boundary). These critical values determine where the actual sample mean would need to fall for the null hypothesis to be rejected at the 0.05 level of significance.
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