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An example of Chi-squared Test for the Variance on NIST website (https://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm) goes as follows:

The observed variance for the 100 measurements of gear diameter is 0.00003969 
(the standard deviation is 0.0063). 
We will test the null hypothesis that the true variance is equal to 0.01.

H0:  σ2 = 0.01


Ha:  σ2 ≠ 0.01


Test statistic:  T = 0.3903

How was this T calculated to be 0.3903?

According to the formula, the value of the statistic should be: $T=(N-1)(s/σ)^2=99(0.00003969/0.01)=0.392931$

Could someone point out anything that I missed here?

techie11
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1 Answers1

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I think this might be an issue with numerical precision.

This site reports the sample standard deviation as 0.00628, which gives the test statistic:

$$T = (N-1)\frac{s^2}{\sigma_0^2}= 99\frac{0.00628^2}{0.1^2} = 0.3904.$$

The NIST site rounds the sample standard deviation up to 0.0063, then reports the sample variance as $0.0063^2 = 0.00003969$, instead of $0.00628^2 = 0.00003944.$

user51547
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