Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

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 $7.07 .$

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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

$μ_{x^{2}} = d f$

and the standard deviation is calculated as

$σ_{x^{2}} = \sqrt{2 \times d f}$

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

$μ_{x^{2}} = d f$

$= 25$

$\Rightarrow μ_{x^{2}} = 25$

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

$σ_{x^{2}} = \sqrt{2 \times d f}$

$= \sqrt{2 \times 25} = \sqrt{50} = 7.071 \approx 7.07$

$\Rightarrow σ_{x^{2}} = 7.07$

Location	$20 - 29$	$30 - 39$	$40 - 49$	$50$ and over
Niagara Falls	$15$	$25$	$25$	$20$
Poconos	$15$	$25$	$25$	$10$
Europe	$10$	$25$	$15$	$5$
Virgin Islands	$20$	$25$	$15$	$5$

Family Size	Sub & Compact	Mid-size	Full-size	Van & Truck
$1$	$20$	$35$	$40$	$35$
$2$	$20$	$50$	$70$	$80$
$3 - 4$	$20$	$50$	$100$	$90$
$5 +$	$20$	$30$	$70$	$70$

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Introductory Statistics

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

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Introductory Statistics

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

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