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Interpreting a Confidence Interval

APSTAT-185TKP

A $90\%$ confidence interval for an unknown population mean $\mu$ has been calculated as $87±12$.

What is the correct interpretation of this confidence interval?

A

We are $90\%$ confident that the true mean is between $75$ and $99$.

B

There is a $0.9$ probability that the true mean is between $75$ and $99$.

C

$90\%$ of all confidence intervals will be between $75$ and $99$.

D

If we took many samples from this population, $90\%$ of the computed confidence intervals would contain the true mean.

E

$90\%$ of data from the population is between $75$ and $99$.