Question

2. A team of market researchers conducted a study involving 200 inhabitants of the United States to determine what people fear most. The gender of each person polled was noted, and then each was asked which of the following was his or her greatest fear: speaking before a group, heights, bugs/insects, financial problems, sickness/death, and other. The results of the poll are given in the table. Do the data provide sufficient evidence to indicate a relationship between gender and greatest fear? Test at the a=.05 level.

	Speaking before a group	Heights	Bugs/Insects	Financial Problems	Sickness/death	Other
Male	21	10	7	23	15	21
Female	16	22	15	9	18	23

Answer 1

Claim: There is a relationship between gender and greatest fear.

The null and alternative hypothesis is

H0: There is NO relationship between gender and greatest fear.

H1: There is a relationship between gender and greatest fear.

Level of significance = 0.05

Test statistic is

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

	Speaking	Heights	Bugs	Financial	sickness	other	Total
Male	21	10	7	23	15	21	97
Female	16	22	15	9	18	23	103
Total	37	32	22	32	33	44	200

O	E	(O-E)	(O-E)^2	(O-E)^2/E
21	17.945	3.055	9.333025	0.520091
10	15.52	-5.52	30.4704	1.963299
7	10.67	-3.67	13.4689	1.262315
23	15.52	7.48	55.9504	3.605052
15	16.005	-1.005	1.010025	0.063107
21	21.34	-0.34	0.1156	0.005417
16	19.055	-3.055	9.333025	0.489794
22	16.48	5.52	30.4704	1.848932
15	11.33	3.67	13.4689	1.188782
9	16.48	-7.48	55.9504	3.395049
18	16.995	1.005	1.010025	0.059431
23	22.66	0.34	0.1156	0.005102
			Total	14.41

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 2 - 1) * (6 - 1) = 1 * 5 = 5

Critical value = 11.070

Test statistic > critical value we reject null hypothesis.

Conclusion:

There is a relationship between gender and greatest fear.