Question

At one vehicle inspection station, 13 of 52 trucks and 11 of 88 cars failed the emissions test. Assuming these vehicles were representative of the cars and trucks in that area, what is the standard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations?

A) .025
B) .032
C) .049
D) .070
E) .095

Answer 1

Answer: The standard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations is 0.066 approximately 0.070

Therefore the answer is (D) 0.070

Step-by-step explanation:

Given that 13 of 52 trucks and 11 of 88 cars failed the emissions test.

p1 = 13 of 52 trucks

p2 = 11 of 88 cars

Solution:

The standard error (SE) of the sampling distribution difference between two proportions is given by;

SE = √{p(1-p)(1/n1 + 1/n2)}

Where p is termed pooled sample

n1 is the size of sample 1, and

n2 is the size of sample 2.

p = (p1*n1 + p2*n2)/(n1 + n2)

p1 = 13/52 = 0.25

p2 = 11/88 = 0.125

n1 = 52

n2 = 88

p = (0.25*52 + 0.125*88)/(52 + 88)

p = 0.1714

SE = √{0.1714(1-0.1714)(1/52 + 1/88)}

SE = √0.0044

SE = 0.066 the standard error