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?

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 0.070Therefore the answer is (D) 0.070Step-by-step explanation:Given that 13 of 52 trucks and 11 of 88 cars failed the emissions test. p1 = 13 of 52 trucksp2 = 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 samplen1 is the size of sample 1, and n2 is the size of sample 2.p = (p1*n1 + p2*n2)/(n1 + n2)p1 = 13/52 = 0.25p2 = 11/88 = 0.125n1 = 52n2 = 88p = (0.25*52 + 0.125*88)/(52 + 88)p = 0.1714SE = √{0.1714(1-0.1714)(1/52 + 1/88)}SE = √0.0044SE = 0.066 the standard error