I'm reading Probability and Statistical Inference, ninth edition by Hogg and on page 436, he gives an example using the chi-square goodness-of-fit test. How did he find this p-value?
3 Answers
$\begingroup$How did he find this p-value?
Using a standard chi-square table you can say that the p-value is less than $0.005$ as $14.4 >12.84$ tabulated.
This result is enough to take any decision, as it is very very low.
If you want a precise result you have to use a calculator. For example, with Excel, typing +DISTRIB.CHI(14.4;3) you get $p=0.002408$
$\endgroup$ $\begingroup$If $X\sim \chi ^2(3)$, then the p-value is given by $\mathbb P(X>14.4)$. With a table or with software it is easy to obtain the probability $0.0024$.
$\endgroup$ $\begingroup$P-value is a value of quantile function at 14.4.
Quantile function may be found using special tables.
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