Respuesta :
Answer:
The 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is between 22.7994 minutes and 33.1406 minutes. The interpretation is that we are 99% sure that the true mean ommute time of all commuters in Washington D.C. area is between 22.7994 minutes and 33.1406 minutes.
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 Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find 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{10.04}{\sqrt{25}} = 5.1706[/tex]
The lower end of the interval is the mean subtracted by M. So it is 27.97 - 5.1706 = 22.7994 minutes
The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 33.1406 minutes.
The 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is between 22.7994 minutes and 33.1406 minutes. The interpretation is that we are 99% sure that the true mean ommute time of all commuters in Washington D.C. area is between 22.7994 minutes and 33.1406 minutes.
