Question

Historically, the industries with the most complaints to the Better Business Bureau have been banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships. The results for a sample of complaints are contained in the file BBB. Click on the datafile logo to reference the data. a. Construct a frequency distribution for the number of complaints by industry. Category Observed Frequency Bank Cable Car Cell Collection Total b. Using , conduct a hypothesis test to determine whether the probability of a complaint is the same for the five industries. The test-statistic is (to 3 decimals). -value (to 4 decimals) What is your conclusion

Answer 1

χ² = 19

Pvalue = 0.0008 ( 4 decimal places)

WE reject the H0 and conclude that probability of complaint is not the same for the 5 industries

Explanation:

H0 : probability of complaint is the same for the 5 industries.

H1: probability of complaint is not the same for the 5 industries.

Category ____ observed frequency

Bank _______ 26

Cable _______44

Car _________42

Cell _________60

Collection ____ 28

Total ________200

The test statistic ;

χ² = (O - E)² / E

O = Observed Frequency ; E = Expected Frequency

Expected Frequency, E = (1 / n) * total

n = number of industries = 5

Expected frequency, E = (1/5)*200 = 40

Expected frequency is the same for all, thus E for all 5 industries = 40

χ² = Σ(O - E)² / E;

χ² = (26-40)² / 40 + (44-40)² / 40 + (42-40)² / 40 + (60-40)² / 40 + (28-40)² / 40

χ² = 19

At α = 0.05 ; df = n-1 = 4 ; χ²critical = 0.000786

Since Pvalue < α ; WE reject the H0 and conclude that probability of complaint is not the same for the 5 industries.