Question

You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.

Category	Population #1	Population #2
A	10	43
B	69	10

What is the chi-square test-statistic for this data?
χ2=

Answer 1

Data =

Category	Population 1	Population 2	Totals
A	10	43	53
B	69	10	79
Totals	79	53	132

Expected =

Category	Population 1	Population 2	Totals
A	(79/132)*53 =31.72	(53/132)*53 = 21.28	53.00
B	(79/132)*79 = 47.28	(53/132)*79= 31.72	79.00
Totals	79.00	53.00	132.00

χ2 = ∑(observed−expected)2 / expected

χ2 = (10 – 31.75)^2 / 31.75 + ( 69 - 47.28)^2 / 47.28 + (43-21.28)^2 / 21.28 + (10-31.72)^2 / 31.72

χ2 = 14.87 + 9.98 + 22.17 + 14.87

χ2 = 61.89‬

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