A chi-square goodness-of-fit test is to be performed to see if data fit the Poisson distribution. There are 8 categories, and λ must be estimated. How many degrees of freedom should be used?
A) 8
B) 7
C) 6
D) 5
E) 4

Question

Quizplus · Accepted Answer

The degrees of freedom for a chi-square goodness-of-fit test are equal to the number of categories minus the number of estimated parameters. Since we are estimating λ, there is 1 estimated parameter. Therefore, the degrees of freedom would be 8-1=7. However, because we are working with a Poisson distribution, the sum of the observed frequencies must equal the sum of the expected frequencies. This means that once we estimate λ, all of the expected frequencies can be calculated based on the Poisson distribution. Therefore, there are actually no degrees of freedom lost due to estimation of parameters, and the correct answer is 8-1=6.

A Chi-Square Goodness-Of-Fit Test Is to Be Performed to See