Respuesta :
Answer:
The 90% confidence interval is (1408.325 hours, 2115.675 hours).
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{1-0.9}{2} = 0.05[/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]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find M as such
[tex]M = z*s[/tex]
In which s is the standard deviation of the sample. So
[tex]M = 1.645*215 = 353.675[/tex]
The lower end of the interval is the mean subtracted by M. So it is 1762 - 353.675 = 1408.325 hours.
The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 2115.675 hours.
The 90% confidence interval is (1408.325 hours, 2115.675 hours).
