Respuesta :
Answer:
The margin of of error for a 95% confidence interval for the population mean is of 1.39 years.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Population standard deviation of 3 years
This means that [tex]\sigma = 3[/tex]
Sample of 18 voters
This means that [tex]n = 18[/tex]
Margin of error:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.96\frac{3}{\sqrt{18}}[/tex]
[tex]M = 1.39[/tex]
The margin of of error for a 95% confidence interval for the population mean is of 1.39 years.
