Question

When performing a test for independence in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statistic in each of the following circumstances. a. a=0.05, r=4, c=5 d. a=0.01, r=3, c=4 e. α=0.01, r=4, c=5 b. a=001, r= 5, c=6 ca=001, r= 5, c=4 a. Determine the upper-tail critical value of the test statistic using the values given in the problem statement for part (a). The critical value is (Type an integer or a decimal Round to three decimal places as needed.)

Answer 1

To find the upper-tail critical value of the test statistic in a contingency table, calculate the degrees of freedom and use a chi-square critical values table.

Step-by-step explanation:

To determine the upper-tail critical value of the test statistic in a contingency table, we first need to find the degrees of freedom (df). The formula to calculate df is df = (number of rows - 1)(number of columns - 1). In the given problem statement for part (a), r = 4 and c = 5, so df = (4 - 1)(5 - 1) = 3 * 4 = 12.

Next, we can use a chi-square critical values table to find the upper-tail critical value for a given significance level. Since a = 0.05, we look for the critical value in the row corresponding to 0.05 and the column corresponding to df = 12.

From the table, we find that the critical value is approximately 21.026, rounded to three decimal places.