Question

In an activity wheel, rats were either isolated or put together and maintained on a restricted feeding schedule. After 25 days, the 30 rats were either alive with stabilized weights or they were dead.

Test for the independence of these two conditions with a X2 test.

Use an a = .01.

Isolated Together

Alive 9 8

Dead 1 12

Answer 1

The null and alternate hypothesis are:

H0: Isolation and death are independent.
Ha: Isolation and death are not independent.

Observed (Oi):

	Isolated	Together	TOTAL
Alive	9	8	17
Dead	1	12	13
TOTAL	10	20	30

Now, Expected frequency = [(Row total) x (Column total)] / Table total

Expected (Ei):

	Isolated	Together	TOTAL
Alive		11.33	17
Dead	4.33	8.67	13
TOTAL	10	20	30

Test statistic value =

The critical value is given by:

Since the test statistic value is greater than the critical value, so we have sufficient evidence to reject null hypothesis H0. Thus, we can say that the two conditions are independent.