Question

The Department of Labor would like to investigate if a difference exists in the proportion of men and women who are currently unemployed. A random sample of 150 men found that 15 were unemployed, and a random sample of 100 women found that 7 were unemployed. Perform a chi-square test for the Department of Labor using α = 0.01.

Answer 1

Following table shows the 2 by 2 table:

	Unemployed	Employed	Total
Men	15	135	150
Women	7	93	100
Total	22	228	250

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	Unemployed	Employed	Total
Men	13.2	136.8	150
Women	8.8	91.2	100
Total	22	228	250

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
15	13.2	0.245454545
7	8.8	0.368181818
135	136.8	0.023684211
93	91.2	0.035526316
Total		0.67284689

The test statistics is:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(2-1)=1

The p-value is: 0.4121

Since p-value is greater than α = 0.01 so we cannot conclude that there is a difference exists in the proportion of men and women who are currently unemployed.