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Q.1

Expert-verified
Found in: Page 652

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# If the number of degrees of freedom for a chi-square distribution is 25, what is the population mean and standard deviation?

When the number of degrees of freedom for a chi-square distribution is $25,$ the population mean is $25$ and the standard deviation is $7.07.$

See the step by step solution

## Given information

Given in the question that, We need to find the population mean and standard deviation if the number of degrees of freedom for a chi-square distribution is$25$.

## Explanation

The population mean in a chi-square distribution is given as

${\mu }_{{x}^{2}}=df$

and the standard deviation is calculated as

${\sigma }_{{x}^{2}}=\sqrt{2×df}$

The degree of freedom is now set to$25$ in the question, and the population mean is determined as follows:

${\mu }_{{x}^{2}}=df$

$=25$

$⇒{\mu }_{{x}^{2}}=25$

Also known as standard deviation, it is determined as follows:

${\sigma }_{{x}^{2}}=\sqrt{2×df}$

$=\sqrt{2×25}\phantom{\rule{0ex}{0ex}}=\sqrt{50}\phantom{\rule{0ex}{0ex}}=7.071\phantom{\rule{0ex}{0ex}}\approx 7.07$

$⇒{\sigma }_{{x}^{2}}=7.07$