How to find the p-value in the chi-square test

Question

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?

Answer 1

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 $p=0.002408$

Answer 2

P-value is a value of quantile function at 14.4.

Quantile function may be found using special tables.

Answer 3

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 $0.0024$.

Answer 4

As mentioned by $tommik$, it's true but you don't need to exactly look at the Critical Value at 5%. Only thing, you have to look at is that, at the value of n = 3, for what value of $\alpha$, it is equal to q = 14.4 and that gives p = 0.002408.