Question

A political scientist wanted to see if there is a relationship between political party identification of college students and support for the legalization of cannabis. The results are presented below. Set alpha = 0.05.

	Support	Does Not Support
Republicans	17	23
Democrats	33	7
Independents	25	15

Step 1: State your null and alternative hypotheses in words

Step 2: Set up the criteria for making a decision. That is, find the critical value.

Step 3: Summarize the data into the appropriate test-statistic.

Step 4: Evaluate the null hypothesis. (Reject or Fail to Reject)

Step 5: What is the interpretation of your findings?

Answer 1

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - political party identification and political party identification are independent Ha​: The two variables - political party identification and political party identification are dependent This corresponds to a Chi-Square test of independence. (2) Critical value and Rejection Region Based on the information provided, the significance level is α=0.05 , the number of degrees of freedom is df = (3 - 1) * (2 - 1) = 2 , so the critical value is 5.9915. Then the rejection region for this test becomes R={χ2:χ2>5.9915}. (3)Test Statistics The Chi-Squared statistic is computed as follows: P-value The corresponding p-value for the test is p=Pr(χ2​>13.6533)=0.0011 (5)Decision about the null hypothesis Since it is observed that χ2=13.6533>χ2_c​rit=5.9915, it is then concluded that the null hypothesis is rejected. (6)Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.05 significance level.

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