Question

An insurance company selected a random sample of 500 clients under 18 years of age and found that 180 of them had had an accident in the previous year. A random sample of 600 clients aged 18 and older was also selected and 150 of them had had an accident in the past year. We want to estimate how much the accident proportions differ between the two age groups.

Answer 1

Answer: The accident proportion differ between the two age groups is 0.11.

Step-by-step explanation:

Since we have given that

Number of clients under 18 years of age = 500

Number of clients had had an accident = 180

Proportion of client had an accident = $\dfrac{180}{500}=\dfrac{18}{50}$

Number of clients aged 18 and older = 600

Number of clients had had an accident = 150

Proportion of client had an accident = $\dfrac{150}{600}=\dfrac{15}{60}$

So, According to question, we get that

Difference between the two age groups proportions would be :

$\dfrac{18}{50}-\dfrac{15}{60}\\\\=\dfrac{108-75}{300}\\\\=\dfrac{33}{300}\\\\=\dfrac{11}{100}$

Hence, the accident proportion differ between the two age groups is 0.11.