Confidence Intervals for the Mean

This section explains the need for confidence intervals and why a confidence interval is not the probability the interval contains the parameter. Then, it discusses how to compute a confidence interval on the mean when sigma is unknown and needs to be estimated. It also explains when to use t-distribution or a normal distribution. Next, it covers the difference between the shape of the t distribution and the normal distribution and how this difference is affected by degrees of freedom. Finally, it explains the procedure to compute a confidence interval on the difference between means.

Confidence Intervals Introduction


Question 1 out of 2.
Strictly speaking, what is the best interpretation of a 95% confidence interval for the mean?
If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean.

A 95% confidence interval has a 0.95 probability of containing the population mean.

95% of the population distribution is contained in the confidence interval.

Question 2 out of 2.
Confidence intervals can only be computed for the mean.