Question

To determine the average lifespan of the African bull elephant, a zoologist collects data on 15 bull elephants. The following table shows the lifespan,
in years, of 15 African bull elephants. Assume lifespans to be normally distributed.
15.2 23.1 7.5 27.3 25.6
37.1 31.4 36.1 24 .1 27.1
26.7 28.4 9.4 21.9 20.9

In class, we concluded:
Based on this sample, we are 90% confident that the mean lifespan of all African bull
elephants is between 20.277 and 27.963 years.
(a) Use clear, complete sentences to explain why a different sample would produce a different
confidence interval for the mean lifespan of all African bull elephants.
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(b) Determine what percentage of the ages in the sample are in the 90% confidence interval. For
example, the first African bull elephant lived 15.2 years, which is not in the confidence interval
(20.277, 27.963). Hint: Check each of the 15 African bull elephants.

(c) Is your answer in part (b) close to 90%? Should it be close to 90%? Use clear, complete
sentences to explain why your answer should or should not be close to 90%.
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Answer 1