Question

Which of the following statements is true in the context of a chi-square goodness-of-fit test?

Select one:

a. The degrees of freedom for determining the critical value will be the number of categories minus 1.

b. A very large test statistic will result in the null not being rejected.

c. The null hypothesis will be rejected for a small value of the test statistic.

d. The critical value will come from the standard normal table if the sample size exceeds 30.

Answer 1

Critical value of the chi-square test depends on the how many categories we have and not on the size of the sample. The higher the value of the test-statistic of chi-square the greater is the chance of rejecteing the null hypothesis

So Options B and C are wrong

For option A the degrees of freedom is (R-1) * (C-1) where R is number of rows and C is number of columns. So option A is wrong

The critical value for a chi-square test will come from the standard normal table if the sample size exceeds 30, that is when chi square is approximately normal

So Option D is true