Answer:
The 95 percent confidence for μ is (63.4292, 64.1708).
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].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find M as such
[tex]M = z*\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{3.08}{\sqrt{265}} = 0.3708[/tex]
The lower end of the interval is the mean subtracted by M. So it is 63.8 - 0.3708 = 63.4292
The upper end of the interval is the mean added to M. So it is 63.8 + 0.3708 = 64.1708
The 95 percent confidence for μ is (63.4292, 64.1708).
