Question

An electronics company manufactures the same product in 3 different locations and ships that product to customers around the world. Sales representatives were experiencing complaints from customers about the performance of the product so they began collecting data. Data was collected about the customers that had experienced a problem with the product and the location the product was manufactured. Determine if there is a relationship between the manufacturing location and whether there was a customer complaint. Select the appropriate conclusion.

Customer Complaints

Location	YES	NO
Location 1	100	70
Location 2	40	20
Location 2	55	15

Select one:

a. At a fixed alpha of 0.02 there is a significant relationship between manufacturing location and customer complaints. Location and complaints are not independent.

b. At the calculated p-value of 0.01 there is a significant significant relationship between manufacturing location and customer complaints. Location and complaints are not independent.

c. At the calculated p-value of 0.10 there is NOT a significant relationship between manufacturing location and customer complaints. Location and complaints areindependent.

d. At a fixed alpha of 0.05 there is NOT a significant relationship between manufacturing location and customer complaints. Location and complaints areindependent.

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	Location 1	110.50	59.50	170
	Location 2	39.00	21.00	60
	Location 3	45.50	24.50	70
	total	195	105	300
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	Location 1	0.9977	1.8529	2.8507
	Location 2	0.0256	0.0476	0.0733
	Location 3	1.9835	3.6837	5.6672
	total	3.0069	5.5842	8.5911
test statistic X2 =		8.5911
p value =		0.0136

since 0.01 < p value  < 0.02

option A is correct

a. At a fixed alpha of 0.02 there is a significant relationship between manufacturing location and customer complaints. Location and complaints are not independent