Question

Students at several large universities took the survey described below. One of the survey questions asked “Where do you sit in class (Front, Middle, Back). Some of the results are shown in the two-way table below.

	Where Do You Sit in Class
		Front	Middle	Back	Row totals
Are You A Male or Female	Female	37	91	22	150
	Male	15	46	25	86
	Total	52	137	47	236

Does this survey data suggest that there is an association between gender and whether the student sits at the back of class?

Answer 1

Observed Frequencies
	Front	Middle	Back	Total
Female	37	91	22	150
Male	15	46	25	86
Total	52	137	47	236
Expected Frequencies
	Front	Middle	Back	Total
Female	52 * 150 / 236 = 33.0508	137 * 150 / 236 = 87.0763	47 * 150 / 236 = 29.8729	150
Male	52 * 86 / 236 = 18.9492	137 * 86 / 236 = 49.9237	47 * 86 / 236 = 17.1271	86
Total	52	137	47	236
	(fo-fe)²/fe
Female	(37 - 33.0508)²/33.0508 = 0.4719	(91 - 87.0763)²/87.0763 = 0.1768	(22 - 29.8729)²/29.8729 = 2.0749
Male	(15 - 18.9492)²/18.9492 = 0.823	(46 - 49.9237)²/49.9237 = 0.3084	(25 - 17.1271)²/17.1271 = 3.619

Null and Alternative hypothesis:

Ho: There is no association between gender and whether the student sits at the back of class

H1: There is an association between gender and whether the student sits at the back of class

Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 7.4739

df = (r-1)(c-1) = 2

p-value:

p-value = CHISQ.DIST.RT(7.4739, 2) = 0.0238

Decision:

p-value < α, Reject the null hypothesis.

There is enough evidence to conclude that there is an association between gender and whether the student sits at the back of class.