Assume that a population mean is μ = 37.8. From a sample, you compute a 95% confidence interval for μ that equals (38.5, 42.5). Your methods would not necessarily be incorrect. Explain in terms of the confidence level.

Question

Assume that a population mean is μ = 37.8.  From a sample, you compute a 95% confidence interval for μ that equals (38.5, 42.5).  Your methods would not necessarily be incorrect.  Explain in terms of the confidence level.

jim_thompson5910 · Answer

The 95% confidence level means that if you generate 100 confidence intervals, then 95 of them will have the population mean 37.8 in them somewhere.

But this confidence interval (38.5, 42.5) does not have the mean 37.8 in it. Sure it's possible to generate a confidence interval that doesn't have the mean in it, but this is a 5% chance, which is pretty small.