Question

A survey of 100 men and 100 women revealed that 15 of the men and 36 of the women were more than 20% overweight. Prepare a contingency table and test the hypothesis that the two gender groups are homogeneous with respect to being overweight. Please assume an α=.05

Answer 1

The contingency table is:

Overweight?	Yes	No	Total
Men	15	85	100
Women	36	64	100
Total	51	149	200

The hypothesis being tested is:

H0: The two gender groups are homogeneous with respect to being overweight

Ha: The two gender groups are not homogeneous with respect to being overweight

		Yes	No	Total
Men	Observed	15	85	100
	Expected	25.50	74.50	100.00
	O - E	-10.50	10.50	0.00
	(O - E)² / E	4.32	1.48	5.80
Women	Observed	36	64	100
	Expected	25.50	74.50	100.00
	O - E	10.50	-10.50	0.00
	(O - E)² / E	4.32	1.48	5.80
Total	Observed	51	149	200
	Expected	51.00	149.00	200.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	8.65	2.96	11.61
		11.61	chi-square
		1	df
		.0007	p-value

The p-value is 0.0007.

Since the p-value (0.0007) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the two gender groups are not homogeneous with respect to being overweight.

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