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blagie [28]
3 years ago
6

Automobile mechanics conduct diagnostic tests on 150 randomly selected new cars of particular make and model to determine the ex

tent 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?
Mathematics
1 answer:
Archy [21]3 years ago
8 0

Answer:

\mathbf{Margin\;  of\;  error} =  .0942816

Step-by-step explanation:

Given

Sample size n = 150

Sample proportion {\widehat{(p)} = \frac{42}{150} = 0.28

Confidence interval = \frac{99}{100} = .99

Margin\;  of\;  error = z_{\frac{\alpha }{2}}\sqrt{\frac{{\widehat{(p)}}{(1 - \widehat{p})}}{n}}

\alpha = 1 - confidence interval = 1 - 0.99 = .01

margin\;  of\;  error = z_{\frac{.01 }{2}}\sqrt{\frac{(.28) (1 - 0.28)}{150}    

For 99\% confidence interval

        ( Z = 2.576 )

margin\;  of\;  error = z_{.005 }}\sqrt{\frac{(.28) (1 - 0.28)}{150}                  

margin\;  of\;  error = 2.576\times\sqrt{\frac{(.28) (1 - 0.28)}{150}

                           =  .0942816

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