Critical Values

Criterion: Explain changes in critical value based on calculations.

Instructions: Read the following and answer the questions.

The chi-square table. The degrees of freedom for a given test are listed in the column to the far left; the level of significance is listed in the top row to the right. These are the only two values you need to find the critical values for a chi-square test.

Work through the following exercise and write down what you see in the chi-square table. This will help familiarize you with the table.

Increasing k and a in the chi-square table

1.Record the critical values for a chi-square test, given the following values for k at each level of significance:

0.10 0.05 0.01

k = 10 ___ ___ ___

k = 16 ___ ___ ___

k = 22 ___ ___ ___

k = 30 ___ ___ ___

Note: Because there is only one k given, assume this is a goodness-of-fit test and compute the degrees of freedom as (k 1).

As the level of significance increases (from .01 to .10), does the critical value increase or decrease? Explain. ___________________________________

As k increases (from 10 to 30), does the critical value increase or decrease? Explain your answer as it relates to the test statistic. ___________________________________