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

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

55? i think maybe

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b