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 in the table. 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 At the .10 significance level, can we conclude that there is a difference in the amounts quoted? a. What are the null and alternate hypotheses? multiple choice 1 a) H0: μd = 0 H1: μd ≠ 0 b) H0: μd ≠ 0 H1: μd = 0 c) H0: μd = 0 H1: μd = 0 b. Compute the test statistic. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.) c. Compute the p-value. NOTE: P-value calculators are available through online search. (Round your answer to 4 decimal places.) d. What is your decision regarding the null hypothesis? multiple choice 2 a) Reject H0 b) Do not reject H0 e. Interpret the result. There is _________ in the mean insurance price.

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Description: 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, a

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

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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 in the table.

	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

At the .10 significance level, can we conclude that there is a difference in the amounts quoted?

a. What are the null and alternate hypotheses?

multiple choice 1

a) H₀: μ_d = 0 H₁: μ_d ≠ 0

b) H₀: μ_d ≠ 0 H₁: μ_d = 0

c) H₀: μ_d = 0 H₁: μ_d = 0

b. Compute the test statistic. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)

c. Compute the p-value. NOTE: P-value calculators are available through online search. (Round your answer to 4 decimal places.)

d. What is your decision regarding the null hypothesis?

multiple choice 2

a) Reject H₀

b) Do not reject H₀

e. Interpret the result.

There is _________ in the mean insurance price.

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