contestada

Automobile mechanics conduct diagnostic tests on 150 randomly selected 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?

Respuesta :

Answer:

[tex]\mathbf{Margin\; of\; error} =[/tex]  .0942816

Step-by-step explanation:

Given

Sample size n = 150

Sample proportion [tex]{\widehat{(p)}[/tex] = [tex]\frac{42}{150}[/tex] = 0.28

Confidence interval = [tex]\frac{99}{100}[/tex] = .99

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

[tex]\alpha =[/tex] 1 - confidence interval = 1 - 0.99 = .01

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

For 99[tex]\%[/tex] confidence interval

        ( Z = 2.576 )

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

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

                           =  .0942816

Otras preguntas