Automobile mechanics conduct diagnostic tests on 150 new cars of particular make and model to determine the extent to which they are affected by a recent recall due to
Faulty catalytic converters. They find that 42 of the new cars tested do have faulty
Catalytic converters. The 99% confidence interval for the true proportion of new cars
With faulty catalytic converters is
A) 0.1856 to 0.3744
B) 0.2434 to 0.3166
C) 0.2081 to 0.3519
D) 0.1660 to 0.3940
E) 0.1243 to 0.4123

Question

Quizplus · Accepted Answer

The sample size is 150, and 42 of the new cars tested do have faulty catalytic converters. So, the sample proportion is 42/150 = 0.28. The standard error of the proportion is sqrt(0.28 * 0.72 / 150) = 0.04. The 99% confidence interval for the true proportion of new cars with faulty catalytic converters is 0.28 +/- 2.576 * 0.04 = 0.28 +/- 0.104 = (0.176, 0.384).

Automobile Mechanics Conduct Diagnostic Tests on 150 New Cars of Particular