Respuesta :
Answer:
The margin of error is of 0.1282 = 12.82%.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A survey conducted by General Motors of 38 drivers in America, 34 indicated that they would prefer a car with a sunroof over one without.
This means that [tex]n = 38, \pi = \frac{34}{38} = 0.8947[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
What is the margin of error?
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 2.575\sqrt{\frac{0.8947*0.1053}{38}} = 0.1282[/tex]
The margin of error is of 0.1282 = 12.82%.
