Answer :
Answer:
a) The critical value is [tex]z = 2.575[/tex].
b) The 99% confidence interval for the mean repair cost for the TVs is ($66.31, $110.61).
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]. This is our critical value
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
a. Find the critical value that should be used in constructing the confidence interval.
The critical value is [tex]z = 2.575[/tex].
b. Construct the 99% confidence interval. Round your answer to two decimal places.
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. So, in this problem
[tex]M = 2.575*\frac{17.20}{\sqrt{4}} = 22.15[/tex]
The lower end of the interval is the mean subtracted by M. So it is 88.46 - 22.15 = $66.31
The upper end of the interval is the mean added to M. So it is 88.46 - 22.15 = $110.61
The 99% confidence interval for the mean repair cost for the TVs is ($66.31, $110.61).