Answer:
(29.13, 30.07)
Step-by-step explanation:
The first step is finding 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], that is between [tex]Z = 1.64[/tex] and [tex]Z = 1.65[/tex], so we use [tex]z = 1.645[/tex].
Now, find M as such:
[tex]M = z*\frac{\sigma}{\sqrt{n}} = 1.645*\frac{2.5}{\sqrt{75}} = 0.47[/tex]
In which [tex]\sigma[/tex] is the standard deviation and n is the length of the sample
The lower end of the interval is the sample mean subtracted by M. So it is 29.6 - 0.47 = 29.13 hours.
The upper end of the interval is the sample mean added to M. So it is 29.6 + 0.47 = 30.07 hours
The 90% confidence interval is (29.13 hours, 30.07 hours).
The correct answer is:
(29.13, 30.07)
