SOLUTION: In order to estimate the average age of onset of a certain type of disease a researcher collects a sample of 15 people with the disease and produces the following 95% confidence in

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Question 1181286: In order to estimate the average age of onset of a certain type of disease a researcher collects a sample of 15 people with the disease and produces the following 95% confidence interval (83.9219, 90.6782). Find a 99% confidence interval for the average age based on the same data set
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The sample mean is the average of the endpoints of the C.I., thus X-bar+=+%2883.9219+%2B+90.6782%29%2F2+=+87.3.
Now from the initial given, t%5B0.975%5D%2A%28s%2Fsqrt%2815%29%29+=++90.6782+-+87.3+=+3.3782
===> 2.145%2A%28s%2Fsqrt%2815%29%29+=+3.3782 ==> s = 6.1.
Then the new 99% C.I. will be = (82.6112, 91.9888).

The t-probabilities were gotten from https://stattrek.com/online-calculator/t-distribution.aspx.