Mathematics: 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

there are 25 students in the class and 15 who wear glasses....

Automobile mechanics conduct diagnostic tests

aeverettpdzrvo

05.01.2022

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

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