3.6 Interpretation of CIs: Answer

3 is the only correct interpretation.

3 is correct as it is a statement conditional on the interval: 95% of intervals constructed in a similar way to the given interval (i.e. through repeated sampling from the population) would be expected to cover (or contain) the true population mean.

1 is incorrect as the confidence interval refers to the population mean, not the sample. 2 is incorrect because the population mean is fixed (and unknown) - the confidence interval either covers this mean or it does not. These points are subtle, but important to understand.