Question

Suppose you have constructed a 90% confidence interval of a population mean, (19.7, 21.2). Decide which statement below is the correct interpretation of the results. Justify your choice, with as much detail as possible.

-With 90% confidence, the mean is in the interval (19.7,21.2).

-There is a 90% probability that the actual mean will be in the interval (19.7,21.2).

Answer 1

I think that the first statement is the correct  interpretation of the results.

This is because we have calculated a 90% confidence interval, i.e. we have calculated an interval or data range for the population mean with 90% confidence level.

So, we can say that with 90% confidence, the mean is in the interval (19.7,21.2)

We can also write it as "90% of total confidence intervals would contain population mean within the range (19.7,21.2)"

Second statement is not correct  interpretation of the results because we are not calculating probability, but we are calculating a confidence interval with 90% level. So, we cant say that there is 90% probability because if wo do so, then we are comparing probability with confidence interval.

We know that probability and confidence interval are not the same things. So, second statement is incorrect.