An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below. We are interested in determining if the accident proportions differ between the two age groups.
The pooled estimator of the population proportion is
A) .305.
B) .300.
C) .027.
D) .450.

Question

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below.  ​ We are interested in determining if the accident proportions differ between the two age groups.
The pooled estimator of the population proportion is
A) .305. 
B) .300. 
C) .027. 
D) .450.

Quizplus · Accepted Answer

To find the pooled estimator of the population proportion, we first calculate the total number of accidents and the total number of clients in each age group:

Under 18: 125 accidents out of 410 clients (proportion = 125/410 = 0.305)
Over 18: 110 accidents out of 365 clients (proportion = 110/365 = 0.301)

We then use the formula for the pooled estimator:

pooled estimator = (number of accidents in Group 1 + number of accidents in Group 2) / (number of clients in Group 1 + number of clients in Group 2)

pooled estimator = (125 + 110) / (410 + 365)
pooled estimator = 235 / 775
pooled estimator = 0.303

Therefore, the closest option to the pooled estimator is B) 0.300.

An Insurance Company Selected Samples of Clients Under 18 Years