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Chi Square Hypothesis Tests -Two Way Tables

Example:
A school district is considering modifying their graduation requirements to include study of a foreign language. They survey a random sample of students with the following results:

How many years of foreign language study should be required for graduation?

		Class        Zero    One    Two  
		Sophomore      37     32     22
		Junior         39     36     27
		Senior         27     31     41

Does the preference of language requirements vary significantly between classes or could the observed differences between classes be explained by the variation that accompanies random samples? What is the probability of results similar to those observed if there is no difference in preferences between classes?

Solution:
You can answer those by using c2 - test. First of all, you will need to enter the data in matrix. From the main menu, press "3" (MAT), then specify the number of rows, and the number of columns. Enter the data.

To perform the chi square test, from the statistical data list, press "F3" (TEST), and then press "F3" (CHI). Next, specify the matrix that contains the data. Press "F1" (CALC) to calculate and press "F6" (DRAW) to draw. Notice that the expected values are in answer matrix.

If class and language requirement preference are independent, the probability of results like those observed is about 0.07. Since this is a slightly large probability, you do not have enough evidence to reject the null hypothesis and assume that class status and language requirement preferences are independent.