Hypothesis test for the difference between two means.
The president of the American Insurance Institute wants to compare the yearly costs of auto insurance offered by two leading companies. He selects a sample of 15 families, some with only a single insured driver, others with several teenage drivers, and pays each family a stipend to contact the two companies and ask for a price quote. To make the data comparable, certain features, such as the deductible amount and limits of liability, are standardized. The sample information is reported below. At the 0.10 significance level, can we conclude that there is a difference in the amounts quoted?
|
Family
|
Progressive
Car Insurance
|
GEICO
Mutual Insurance
|
|
Becker
|
$2,090
|
$1,610
|
|
Berry
|
1,683
|
1,247
|
|
Cobb
|
1,402
|
2,327
|
|
Debuck
|
1,830
|
1,367
|
|
Dubrul
|
930
|
1,461
|
|
Eckroate
|
697
|
1,789
|
|
German
|
1,741
|
1,621
|
|
Glasson
|
1,129
|
1,914
|
|
King
|
1,018
|
1,956
|
|
Kucic
|
1,881
|
1,772
|
|
Meredith
|
1,571
|
1,375
|
|
Obeid
|
874
|
1,527
|
|
Price
|
1,579
|
1,767
|
|
Phillips
|
1,577
|
1,636
|
|
Tresize
|
860
|
1,188
|