Respuesta :
Answer:
The 98% confidence interval for the population mean is between 17.5 hours and 21.7 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{1-0.98}{2} = 0.01[/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]1-0.01 = 0.99[/tex], so [tex]z = 2.325[/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 = 2.325*\frac{5.8}{\sqrt{42}} = 2.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 19.6 - 2.1 = 17.5 hours
The upper end of the interval is the sample mean added to M. So it is 19.6 + 2.1 = 21.7 hours
The 98% confidence interval for the population mean is between 17.5 hours and 21.7 hours.
