Question

1) Researchers have found that providing therapy dogs on college campuses near midterms and finals is an effective way to reduce student stress. They wondered if providing other animals would also reduce stress. To find out, they brought four different animals to campus and had students rate their stress level after time spent with the animal. The results are presented below.

OBSERVED		Dog	Cat	Ferret	Lizard
More Stressed		18	32	38	92
Same Stressed		30	28	42	40
Less Stressed		132	90	40	18

a) Specify the null and alternative hypotheses for a chi-square test of independence

B)Fill in the table below with the expected frequencies

EXPECTED		Dog	Cat	Ferret	Lizard
More Stressed
Same Stressed
Less Stressed

c) Use the observed and expected frequencies to calculate a chi-square test of independence to detect any relationship between type of animal and feelings of stress, using alpha = .01. Report the critical value and your decision.

e) Calculate the effect size for the relationship between animal type and stress level.

Answer 1

a)

Claim: There is a relationship between animal type and stress level.

The null and alternative hypothesis is

H0: There is no relationship between animal type and stress level.

H1: There is a relationship between animal type and stress level.

Level of significance = 0.01

OBSERVED		Dog	Cat	Ferret	Lizard	Total
More Stressed		18	32	38	92	180
Same Stressed		30	28	42	40	140
Less Stressed		132	90	40	18	280
Total		180	150	120	150	600

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

EXPECTED		Dog	Cat	Ferret	Lizard
More Stressed		54	45	36	45
Same Stressed		42	35	28	35
Less Stressed		84	70	56	70

c)

O	E	(O-E)	(O-E)^2	(O-E)^2/E
18	54	-36	1296	24
32	45	-13	169	3.755556
38	36	2	4	0.111111
92	45	47	2209	49.08889
30	42	-12	144	3.428571
28	35	-7	49	1.4
42	28	14	196	7
40	35	5	25	0.714286
132	84	48	2304	27.42857
90	70	20	400	5.714286
40	56	-16	256	4.571429
18	70	-52	2704	38.62857
			Total	165.84

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 3 - 1) * (4 - 1) = 2 * 3 = 6

Critical value = 16.182

( From chi-square table)

Critical value < test statistic we reject the null hypothesis.

Conclusion:

There is a relationship between animal type and stress level.

e)

The effect size for the relationship between animal type and stress level is:

df^* = Smaller of ( ( r - 1) , ( c - 1 ) ) = ( ( 3 - 1) , ( 4 - 1) ) = 2