Respuesta :
Answer:
The 99% confidence interval for the mean distance from home to work for all residents of this state is between 8.49 and 9.19 miles.
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 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[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.
[tex]M = 2.575\frac{2.7}{\sqrt{400}} = 0.35[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 8.84 - 0.35 = 8.49 miles.
The upper end of the interval is the sample mean added to M. So it is 8.84 + 0.35 = 9.19 miles.
The 99% confidence interval for the mean distance from home to work for all residents of this state is between 8.49 and 9.19 miles.
