statistic and probabilities

Question

you are conducting a multinomial chi-square goodness of fit hypothesis teat for the claim that the 4 categories occur with the following frequencies:

observed frequency: A-41

B-21

C-30

D-29

what is the chi-square test statistic for this data?

what is the p-value?

Answer 1

This question is worded poorly. I presume that the null hypothesis is that the probability of each of the four groups is equal. (41+21+30+29)/4 = 30.25

Then, ((41-30.25)^2 + (21 - 30.25)^2 + (30-30.25)^2 + (29-30.25)^2)/30.25 = 6.70247933884298

As there are four groups, we have three degrees of freedom.

Then, we get the p-value in Excel using =CHISQ.DIST.RT(6.70247933884298,3) = 0.0820102820452275

We can actually let Excel do the calculation for us using

=CHISQ.TEST({41,21,30,29},{30.25,30.25,30.25,30.25}) ; you can point to cells with the values rather than entering them in the formula. This bypasses the calculation of the test statistic and just returns the p-value.