Will our interval estimate include the population mean?

Consider an interval estimate of a population mean, µ, centred on the mean of a random sample, . If we reduce the width of this interval estimate, we become less confident that the interval will include the unknown value of µ.

The confidence level quantifies this

How can we quantify our confidence that an interval will include the target population parameter? Consider an interval estimate for µ of the form

where the constant tn−1 is obtained from a table or graph. The diagram below shows the appropriate value of this constant for various sample sizes.

For reasons that cannot be explained here, you must look up the t-value using the sample size minus one rather than the sample size itself. The value n - 1 is called the degrees of freedom of the constant.

Click on a cross to display its degrees of freedom and read off the t-value. Alternatively, type a value into the degrees of freedom box under the graph then hit the return key on your keyboard. Note that