Question

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 data for the sample of families and their two insurance quotes are reported below.

At the 0.10 significance level, can we conclude that there is a difference in the amounts quoted? Hint: For the calculations, assume the "Midstates Car Insurance" as the first sample.

	Midstates Car				Gecko Mutual
Family	Insurance				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

1. State the decision rule for 0.10 significance level: H₀: μ_d = 0 H₁: μ_d ≠ 0. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

Reject H0 if T< _______ or t> _________

2. Compute the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

The test statistic is ___________

3. State your decision about the null hypothesis.

- Do not reject H0

- Reject H0

Answer 1

Using Excel: Go to Data, select Data Analysis,choose t-Test: Two-Sample Assuming Unequal Variances, in the following way:

t-Test: Two-Sample Assuming Unequal Variances
	Car Insurance	Gecko Mutual Insurance
Mean	1390.8	1637.133333
Variance	191630.4571	89437.55238
Observations	15	15
Hypothesized Mean Difference	0
df	25
t Stat	-1.799546628
P(T<=t) one-tail	0.042007176
t Critical one-tail	1.316345073
P(T<=t) two-tail	0.084014353
t Critical two-tail	1.708140761

H0: μd = 0

H1: μd ≠ 0

T:p-value=0.084

Test statistic: t = -1.7995

Critical value (Using Excel function T.INV.2T()) =T.INV.2T(0.10,25) =1.708

Since test statistic is less than critical value, we do not reject the null hypothesis and conclude that mean yearly costs of insurence for the wo companies is the same.

Ans 1: Reject H0 if T<0.10 or t >1.708.

Ans 2: Test statistic= -1.80

Ans 3: Do not reject H0.