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 : [tex]\hat{p}=\dfrac{42}{150}=0.28[/tex]
Critical value of z for 99% confidence level : [tex]z_{\alpha/2}=2.576[/tex]
Formula for Margin of error :
[tex]E=z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]E=(2.576)\sqrt{\dfrac{0.28(1-0.28)}{150}}\\\\=0.0944377199216\approx0.0944\ \text{Rounded to four decimal places}[/tex]
Hence, the required margin of error = [tex]0.0944[/tex]
