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

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}=(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{\frac{\hat{p}(1-\hat{p})}{n}}`

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

Hence, the required margin of error =
`0.0944`