**Hypothesis Testing and Degrees of Freedom**In this educational example, a researcher conducts a hypothesis test using a sample size of \( n = 20 \) with a sample mean \( M = 34 \) and a sample variance \( s^2 = 36 \) from an unknown population. The question posed is: What is the degrees of freedom (\( df \)) value for the \( t \) statistic?The options provided are:- \( df = 19 \)- \( df = 35 \)- \( df = 21 \)- \( df = 37 \)**Explanation:**In statistical testing, the degrees of freedom for a single-sample t-test is calculated using the formula:\[df = n - 1\]Given that the sample size \( n = 20 \), we can determine the degrees of freedom as follows:\[df = 20 - 1 = 19\]Therefore, the correct answer is \( df = 19 \). This value is crucial for determining the critical value from the \( t \)-distribution table to assess statistical significance.

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A researcher conducts a hypothesis test uUsing a sample of n= 20 with M 34 and s = 36 from an unknown population. What is the df value for the t statistic? O df = 19 O df = 35 O df = 21 df = 37