Final answer:
In order to test for the independence of the row and column variables, we can use the chi-square test of independence. We compare observed and expected frequencies to assess if there is a significant association between the variables.
Step-by-step explanation:
To test for independence of the row and column variables, we can use the chi-square test of independence. The null hypothesis for this test states that the two variables are independent. The test compares observed values to expected values. In this case, each cell category should have an expected value of at least five.
To perform the test, we calculate the chi-square statistic using the formula:
x² = Σ (O - E)² / E
where O is the observed frequency and E is the expected frequency for each cell.
Then, we compare the calculated chi-square value to the critical value from the chi-square distribution table with degrees of freedom equal to (number of rows - 1) * (number of columns - 1). If the calculated chi-square value is greater than the critical value, we reject the null hypothesis and conclude that the variables are dependent.
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The following table contains observed frequencies for a sample of 200 .
Rowvariable Column variable
A B C
P 20 44 50
Q 30 26 30
Test for independence of the row and column variables using α=0.05.