Question

Question No 3. Tests Using Contingency Tables:

A researcher selected sample of customs from 4 companies and asked them if the companies care give warranty on sold items or not. Assume observed values from your own (fill the below table by assuming any values of your choice) and test the claim that the proportion of customers of each company who got warranty is the same for each company by choosing alpha of your own choice. (Marks 2.5)

	Company A	Company B	Company C	Company D	Total
Warranty: Yes	55	60	25	30	170
Warranty: No	14	22	18	10	64
Total	69	82	43	40	234

A = 0.03

Step 1: HO = u1 = u2 = u3 = u4

At least 1 mean is different from the others

Step 2: : Find the critical value at = 0.03 with (2-1)(4-1) = 3 degree of freedom

D.f = 5-3 = 2 and a = 0.03. CV =

Answer 1

The hypothesis being tested is:

H0: The proportion of customers of each company who got a warranty is the same for each company

Ha: The proportion of customers of each company who got a warranty is not the same for each company

observed	expected	O - E	(O - E)² / E
55	42.500	12.500	3.676
60	42.500	17.500	7.206
25	42.500	-17.500	7.206
30	42.500	-12.500	3.676
170	170.000	0.000	21.765
8.947	critical value
21.76	chi-square
3	df
.0001	p-value

The critical value is 8.947.

df = 4 - 1 = 3

The test statistic is 21.76.

The p-value is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.03), we can reject the null hypothesis.

Therefore, we can conclude that the proportion of customers of each company who got a warranty is not the same for each company.