Question

Crash testing is a highly expensive procedure to evaluate the ability of an automobile to withstand a serious accident. A simple random sample of 12 small cars were subjected to a head-on collision at 40 miles per hour. Of them 8 were “totaled,” meaning that the cost of repairs is greater than the value of the car. Another sample of 17 large cars were subjected to the same test, and 5 of them were totaled. Let p_X represent the population proportion of small cars that are totaled and let p_Y represent the population proportion of large cars that are totaled. Find a 95% confidence interval for the difference p_X – p_Y . Round the answers to four decimal places.

The 95% confidence interval is (  ,  )

Answer 1

Solution :

Given that,

n₁ = 40

x₁ = 12

₁ = x₁ / n₁ = 0.3

n₂ = 17

x₂ = 8

₂ = x₂ / n₂ = 0.4706

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.3 - 0.4706

= -0.1706

2)

Our aim is to construct 95% confidence interval.

= 1.96 (use z table)

Margin of error =   *

=  

= 0.2765

3) Required interval is

Point estimate   Margin of error

-0.1706    0.037734

(-0.1706 - 0.2765 , -0.1706 +  0.2765 )

(-0.4471 , 0.1059)

The 95% confidence interval is (-0.4471 , 0.1059)