Question

In , the industries with the most complaints to the Better Business Bureau were banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships (USA Today, April 16, 2012). The results for a sample of complaints are contained in the DATAfile named BBB.

Category	Observed Frequency
Bank	26
Cable	44
Car	42
Cell	60
Collection	28
Total	200

b. Using , conduct a hypothesis test to determine if the probability of a complaint is the same for the five industries. The test-statistic is? (to 2 decimals). p-value? (to 4 decimals) What is your conclusion?

c. Which industry has the most complaints? Dropping the industry with the most complaints using , conduct a hypothesis test to determine if the probability of a complaint is the same for the remaining four industries. The test-statistic is? (to 2 decimals). P-value? (to 4 decimals) What is your conclusion?

Answer 1

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
Bank	26	0.2	200 * 0.2 = 40	(26 - 40)²/40 = 4.9
Cable	44	0.2	200 * 0.2 = 40	(44 - 40)²/40 = 0.4
Car	42	0.2	200 * 0.2 = 40	(42 - 40)²/40 = 0.1
Cell	60	0.2	200 * 0.2 = 40	(60 - 40)²/40 = 10
Collection	28	0.2	200 * 0.2 = 40	(28 - 40)²/40 = 3.6
Total	200	1.00	200	19

b)

Test statistic:  

χ² = ∑ ((O-E)²/E) = 19

df = n-1 =    4

p-value = CHISQ.DIST.RT(19, 4) = 0.0008  

Decision:  

p-value < α, Reject the null hypothesis  

c) The industry with the most complaints: Cell

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
Bank	26	0.25	140 * 0.25 = 35	(26 - 35)²/35 = 2.3143
Cable	44	0.25	140 * 0.25 = 35	(44 - 35)²/35 = 2.3143
Car	42	0.25	140 * 0.25 = 35	(42 - 35)²/35 = 1.4
Collection	28	0.25	140 * 0.25 = 35	(28 - 35)²/35 = 1.4
Total	140	1.00	140	7.43

Test statistic:  

χ² = ∑ ((O-E)²/E) = 7.43

df = n-1 = 3

p-value = CHISQ.DIST.RT(7.4286, 3) = 0.0594  

Decision:  

p-value > α, Do not reject the null hypothesis.