critical values

Problem Set 4.8: 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: 10 .05 .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). 2. As the level of significance increases (from .01 to .10), does the critical value increase or decrease? Explain. 3. As k increases (from 10 to 30), does the critical value increase or decrease? Explain your answer as it relates to the test statistic