Question

A sample of World Campus students were surveyed. They were asked which of the following they prefer to drink: beer, water, or neither. And, their biological sex was recorded. These data are presented in the table below. [75 points]

	Biological Sex
	Female	Male
Beer	61	137
Wine	144	44
Neither	76	62

H. In this sample, are biological sex and drink preference independent or related? Explain why.

Answer 1

The null and alternative hypothesis is

H0: Biological sex and drink preference independent.

H1: Biological sex and drink not preference independent.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

	Female	Male	Total
Beer	61	137	198
Wine	144	44	188
Neither	76	62	138
Total	281	243	524

O	E	(O-E)	(O-E)^2	(O-E)^2/E
61	106.1794	-45.1794	2041.177	19.22386
137	91.82061	45.17939	2041.177	22.23005
144	100.8168	43.18321	1864.789	18.49681
44	87.18321	-43.1832	1864.789	21.38932
76	74.00382	1.996183	3.984747	0.053845
62	63.99618	-1.99618	3.984747	0.062265
			Total	81.46

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 3 - 1) * (2 - 1) = 2 * 1 = 2
Critical value = 5.991

( From chi-square table)

Test statistic > critical value we reject null hypothesis.

Conclusion:

Biological sex and drink not preference independently.