Question

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 = 900 n2 = 400
Number making claims = 135 Number making claims = 24

Required:
a. Use a level of significance α = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. Explain your determination.
b. Provide a 95% confidence interval for the difference between the proportions for the two populations.

Answer 1

Explanation:

Given the following :

Single policy holders (n1) = 900

Number making claims (x1) = 135

Married Policy holders (n2) = 400

Number making claims (x2) = 24

α = 0.05

a. Use a level of significance α = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. Explain your determination.

Null: p1 - p2 = 0

Alternative : p1 - p2 ≠ 0

p = (n1p1 + n2p2) / n1 + n2 ;

p1 = x1/n1 = 135 / 900 = 0.15

p2 = x2/n2 = 24 / 400 = 0.06

p = (900*0.15 + 400*0.06) / (900 + 400)

p = 0.1223076

Test statistic (z):

(p1 - p2) / √p(1-p)(1/n1 + 1/n2)

(0.15 - 0.06) / √0.12231(1-0.12231)(1/900 + 1/400)

= 4.5710979

Decision:

Reject Null if P < α

Obtaining p value from z score using calculator :

P value = 0.0001

0.0001 < 0.05

Hence,

Reject Null