Suppose that you are performing a $\chi ^ { 2 }$-test for a population standard deviation. Which of the following statements regarding the distribution of the test statistic is true?
A)If the null hypothesis is true, the test statistic has a chi-square distribution with $\mathrm { df } = \mathrm { n }$.
B) If the null hypothesis is true, the test statistic has a chi-square distribution with $\mathrm { df } = \mathrm { n } - 1$.
C) If the null hypothesis is false, the test statistic has a chi-square distribution with $\mathrm { df } = \mathrm { n }$.
D) If the null hypothesis is false, the test statistic has a chi-square distribution with $d f = n - 1$.

Question

Quizplus · Accepted Answer

When performing a $\chi^2$-test for a population standard deviation, if the null hypothesis is true, the test statistic follows a chi-square distribution with degrees of freedom ($df$) equal to the sample size ($n$) minus 1. This accounts for the estimation of one parameter (the standard deviation or variance) from the sample.

Suppose That You Are Performing A χ2\chi ^ { 2 }χ2

Suppose That You Are Performing A $\chi ^ { 2 }$