Question

A school district wants to see if people's opinions about school closings are related to their professions. From a sample of 285 people. The following data was obtained at the alpha= .05 level of significance, test the claim that opinions are independent of profession.

	Teachers	other white collar workers	Blue collar workers	row totals
Favor	14	8	8	30
oppose	105	75	75	255
column totals	119	83	83	285

Answer 1

Chi-Square Independence test - Results

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - Opinions about school closing and professions are independent Ha​: The two variables - Opinions about school closing and professions are dependent This corresponds to a Chi-Square test of independence. (2) Degrees of Freedom The number of degrees of freedom is df = (2 - 1) * (3 - 1) = 2 (3) 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 = (2 - 1) * (3 - 1) = 2, so the critical value is 5.9915. Then the rejection region for this test becomes R={χ2:χ2>5.9915}. (4)Test Statistics The Chi-Squared statistic is computed as follows: (5)P-value The corresponding p-value for the test is p=Pr(χ2​>0.3327)=0.8468 (6)The decision about the null hypothesis Since it is observed that χ2=0.3327<χ2_c​rit=5.9915, it is then concluded that the null hypothesis is NOT rejected. (7)Conclusion It is concluded that the null hypothesis Ho is NOT rejected. Therefore, there is NOT enough evidence to claim that the two variables - Opinions about school closing and professions are dependent, at the 0.05 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive.

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