APFIVE Interpreting a Confidence Interval
A researcher calculates a 95% confidence interval for a population mean and states, “There is a 95% probability that the true mean lies within this interval.” Identify the mistake in this interpretation.
A
The confidence level describes the long‐run success rate of the procedure, not the probability that the true mean is in any one computed interval.
B
The statement is correct; the interval does have a 95% probability of containing the true mean.
C
There is an error only if a t-score should have been used instead of a z-score.
D
The researcher should have expressed the confidence level in percentage points, not probability.
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