Question

You have analyzed data from an experiment with the Chi Square test. You calculate that x2= 11.121 for 5 degrees of freedom (c-1). If you have established the level of significance to be p=0.05, would this result indicate a significant difference between the expected results and the observed results?

Answer 1

The degrees of freedom for a Chi Square test of homogeneity with a five-by-two table is (r-1)(c-1), and the result would indicate a significant difference if the calculated x² is greater than or equal to the critical value at the chosen level of significance.

Step-by-step explanation:

The degrees of freedom for a Chi Square test of homogeneity with a five-by-two table is calculated as (r-1)(c-1), where r is the number of rows and c is the number of columns of the table. In this case, the table has five rows and two columns, so the degrees of freedom would be (5-1)(2-1) = 4.

To determine if the result is significant, we compare the chi-square test statistic (x²) to the critical value at the chosen level of significance (p-value).

If the calculated x² is greater than or equal to the critical value, we reject the null hypothesis and conclude that there is a significant difference between the expected and observed results.

In this case, since the calculated x² is 11.121 and the degrees of freedom (df) is 4, we need to find the critical value from the chi-square distribution table with 4 degrees of freedom at the 0.05 significance level.

If the critical value is greater than or equal to 11.121, then the result would indicate a significant difference.