Please help me quickly. I have a quiz on this and I don't know the answers to this question or how to do all of it

Question

You are conducting a Goodness of Fit hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table. Report all answers correct to three decimal places.

Category	Observed Frequency	Expected Frequency
A	12
B	8
C	7
D	22
E	15

*****The fourth column is (obs-exp)^2/exp, it just didn't show up.*****

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

χ2= __________

Answer 1

Sounds like your null needs to be H₀ : all 5 category means are =, so the expected frequency for each mean is also =, and that is the same as the overall mean of the 'N' people(?) that are choosing a category:

1) Calculate that mean:(12+8+7+15+22)/5 =12.4.

2) This is the value for each of your expected frequencies.

3) Use the equation listed for the 4th column and calculate it for each row.

4) Add those five values is your Chi-squared test, and is also a Goodness-of-Fitness test for a two-way table.

5) Look up your value in a table for a Chi-Square distribution, to get the p-value and answer the question.

If the computed test statistic is large, then the observed and expected values are not close and the model is a poor fit to the data.