Question

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. What is the margin of error for a​ 99% confidence interval based on these sample​ results? (Round to four decimal places.) Group of answer choices

Answer 1

Answer: 0.0944

Step-by-step explanation:

Given : Sample size of cars : n= 150, sample size is greater than 30 , so we use z-test.

Number of cars tested do have faulty catalytic converters =42

Then the proportion of cars   have faulty catalytic converters : $\hat{p}=\dfrac{42}{150}=0.28$

Critical value of z for 99% confidence level : $z_{\alpha/2}=2.576$

Formula for Margin of error :

$E=z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$E=(2.576)\sqrt{\dfrac{0.28(1-0.28)}{150}}\\\\=0.0944377199216\approx0.0944\ \text{Rounded to four decimal places}$

Hence, the required margin of error = $0.0944$