How to solve this (Algebra 2)
1 answer:
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Answer:
(18.1042, 35.2292) is a 90% confidence interval for the mean number of journal articles read monthly by professors.
Step-by-step explanation:
We have a small sample of size n = 12, and s = 16.5163. A pivotal quantity for this case is given by
which has a t distribution with n-1 degrees of freedom if we suppose that we take the sample from the normal population. The confidence interval is given by
where
is the
th quantile of the t distribution with n - 1 = 12 - 1 = 11 degrees of freedom. As we want the 90% confidence interval, we have that
and the confidence interval is
where
is the 5th quantile of the t distribution with 11 df, i.e.,
. Then, we have
and the 90% confidence interval is given by (18.1042, 35.2292).
First, turn the second one into a normal fraction:
Then set the denominators equal:
Solve:
So the answer should be
Then set the denominators equal:
Solve:
So the answer should be