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A large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period. Single Policyholders Married Policyholders n 1 = 400 n 2 = 900 Number making claims = 76 Number making claims = 90 a. Use α = .05. Test to determine whether the claim rates differ between single and married male policyholders. b. Provide a 95% confidence interval for the difference between the proportions for the two populations.

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 10, Problem 44SE
Textbook Problem
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A large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period.

Single Policyholders Married Policyholders
n1 = 400 n2 = 900
Number making claims = 76 Number making claims = 90
  1. a. Use α = .05. Test to determine whether the claim rates differ between single and married male policyholders.
  2. b. Provide a 95% confidence interval for the difference between the proportions for the two populations.

a.

To determine

Test whether the claim rates differ between single and married male policyholders at

α=.05.

Explanation of Solution

Calculation:

The data represents the number of single male and married male policyholders who made an insurance claim over the preceding three-year period.

The data is as follows:

Single PolicyholdersMarried Policyholders
n1=400n2=900
Number making claims=76Number making claims = 90

State the hypothesis:

The test hypotheses are as follows:

Null hypothesis:

H0:p1p2=0

That is, there is no difference between the single and married male policyholders.

Alternative hypothesis:

Ha:p1p20

That is, there is a difference between the single and married male policyholders.

Test statistic:

The test statistic for hypothesis tests about p1p2 is,

z=(p¯1p¯2)p¯

b.

To determine

Obtain 95% confidence interval for the difference between the proportions of the two populations.

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