Presentation 606

Samriti Malhotra
3rd April 2019

Inference of Categorical Data.

Question 6.27: How many categories were there in the juror example? How many degrees of freedom should be associated with the chi-square distribution used for X² ?

Solution

In the jurors example, there were k = 4 categories: white, black, Hispanic, and other.

According to the rule above, the test statistic X² should then follow a chi-square distribution with k - 1 = 3 degrees of freedom if H0 is true.

Just like we checked sample size conditions to use the normal model in earlier sections,we must also check a sample size condition to safely apply the chi-square distribution for X^2.

Each expected count must be at least 5.
In the juror example, the expected counts were 198, 19.25, 33, and 24.75, all easily above 5, so we can apply the chi-square model to the test statistic, X² = 5.89.