Question

An insurance company has been reviewing the performance of the different types of insurance policies it sells. Looking at policies sold in 2018, the insurance company found that out of 850 car insurance policies sold, 322 had claims against them; and for the 924 home polices .sold, 260 had claims against them.

i. Calculate a 95% confidence interval for the proportion of claims made against car insurance policies.

ii. Calculate a 95% confidence interval for the proportion of claims made against home insurance policies.

Answer 1

i)

sample success x =		322
sample size          n=		850
sample proportion p̂ =x/n=		0.3788
std error se= √(p*(1-p)/n) =		0.0166
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.0326
lower bound=p̂ -E                       =		0.346
Upper bound=p̂ +E                     =		0.411

from above 95% confidence interval for population proportion =(0.346,0.411)

ii)

sample success x =		260
sample size          n=		924
sample proportion p̂ =x/n=		0.2814
std error se= √(p*(1-p)/n) =		0.0148
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.0290
lower bound=p̂ -E                       =		0.252
Upper bound=p̂ +E                     =		0.310

from above 95% confidence interval for population proportion =(0.252,0.31)