Question

You obtain a dataset from a random sample. • You double-checked your dataset, and there were no typos, and no errors. • All conditions were met to develop a confidence interval. • You develop a 97% confidence interval for the population mean µ, and your confidence interval is 74.3 < µ < 78.3. • You double-checked your calculations, and everything was done correctly. Question: Later, you find out that the actual population mean is µ = 71. Why doesn’t your confidence interval contain the actual population mean?

Answer 1

Interval is given with 97% confidence. Thus there is 3% probability that interval is not true.

Explanation:

In Statistics, estimated intervals are given with some confidence level. In this example person develop the interval with 97% confidence.

Statistically, this means that the person can be 97% sure (not 100%) that population mean is 74.3 < µ < 78.3. There is still 3% probability that population mean falls outside of the interval.

Small sample size may also lead wrong estimates.