Question

A business needs to know whether customers of different genders have specific favourite colours. Using the following information, develop a contingency table test. Male: 10 blue, 18 red, 22 black Female: 25 blue, 11 red, 14 black At at 0.05 level of significance, use formal hypothesis test to determine whether colour preference of a customer depends on gender.

Answer 1

H0: Null Hypothesis: Color preference of a customer do not depend on gender

HA: Alternative Hypothesis: Color preference of a customer depend on gender

Observed Frequencies:

	Blue	Red	Black	Total
Male	10	18	22	50
Female	25	11	14	50
Total	35	29	36	100

Expected Frequencies:

	Blue	Red	Black	Total
Male	35X50/100=17.50	14.50	18.00	50
Female	17.50	14.50	14=8.00	50
Total	35	29	36	100

Test statistic is calculated as follows:

Observed (O)	Expected (E)	(O - E)2/E
10	17.50	3.21
18	14.50	0.84
22	18.00	0.89
25	17.50	3.21
11	14.50	0.84
14	18.00	0.89
Total = =		9.90

ndf = (r - 1) X (c - 1)

=(2 -1) X (3 - 1) = 2

By Technology, P - value = 0.0071

Since P - Value = 0.0071 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that Color preference of a customer depend on gender.