A6. A survey collected information regarding occupation and voting in a district

Question

A6. A survey collected information regarding occupation and voting in a district. The relationship is examined on a contingency table, which is shown below on table A6.1. Table A6.1 Vote by Occupation*' Occupation White Collar Blue Collar Totals Vote Labour 62 58 52 110 120v 80 Other 28 90 200 Note: Level of significance of .05 will be used to test the hypothesis- State the null and alternative hypotheses for this chi-square approach and state which variable in independent and dependent. Use the chi-square approach to test whether occupation is independent of an individual's vote. Test using = 0.05 level.

Explanation / Answer

Here the independent variable is Occupation and the dependent variable is dependent.

The Hypothesis:

H0: There is no relation between Occupation and individuals vote. i.e they are independent.

Ha: There is a relation between occupation and individuals vote. i.e they are dependent.

The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 200

The degrees of freedom = (r – 1) * (c -1) = (2 - 1) * (2 - 1) = 1

The Test Statistic: The table below gives the calculation of 2.

2test = 5.387

The Critical Value:   The critical value at = 0.05, df = 1

2critical = 3.8414

The Decision Rule: If 2 test is > 2 critical, then Reject H0.

The Decision:    Since If 2 test (5.387) is > 2 critical (3.8414), We Reject/Fail to reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that there is a relation between occupation and individuals vote. i.e they are dependent.

Observed White Collar Blue Collar Total Labour 62 58 120 Other 28 52 80 Total 90 110 200 Expected White Collar Blue Collar Total Labour 54.00 66.00 120 Other 36.00 44.00 80 Total 90 110 200

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