Lab 3: 2x2 Contingency table

For the third lab the class filled in a 2x2 contingency table according to their morning habits: coffee drinker (Y/N) and breakfast eater (Y/N). The table and class data are given below:

		Coffee
		Yes	No	Total
Breakfast	Yes	22	26	48
	No	12	3	15
	Total	34	29	63

The class was asked to perform a test of independence on the data using Cochrane’s correction for continuity.

H₀: Whether someone drinks coffee is independent of whether they eat breakfast

H₀: p_ij = p_i.*p_.j for i=1,…,r, j=1,…,c

H_a: Coffee drinking and breakfast eating are not independent

H_a: p_ij ≠ p_i.*p_.j for at least one i=1,…,r, j=1,…,c

df = 1*1 = 1

χ²_1,.05 = 3.841

The smallest expected count is:

15*29/63 = 6.905, which is greater than f=3

|3-6.905| = 3.905, therefore D=3.5

χ²_c = 63³*3.5²/(34*29*48*15) = 4.305

4.305>3.841, therefore reject H₀.

0.025 < P(χ²₁>4.305) < 0.05

Breakfast eating is not independent of coffee drinking.