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 theStandard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations?
A) 0.070
B) 0.095
C) 0.025
D) 0.049
E) 0.032

Question

Quizplus · Accepted Answer

The standard error of the difference in proportions is calculated using the formula: $\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$, where $p_1$ and $p_2$ are the proportions of the first and second groups, and $n_1$ and $n_2$ are the sizes of the first and second groups, respectively.For trucks, $p_1 = \frac{13}{52}$ and $n_1 = 52$.For cars, $p_2 = \frac{11}{88}$ and $n_2 = 88$.Plugging these values into the formula gives:$\sqrt{\frac{\frac{13}{52}(1-\frac{13}{52})}{52} + \frac{\frac{11}{88}(1-\frac{11}{88})}{88}}$Simplifying this expression gives a standard error of approximately 0.070, which corresponds to choice A.

At One Vehicle Inspection Station, 13 of 52 Trucks and 11