Consider the following problem:

The grade point averages for 12 randomly selected students are shown in the table below. Find the 99% confidence interval around the population mean, µ. Assume the population is normally distributed.

Solution:

This is a small sample, n < 30, and we do not know sigma. Although small samples generally are t-distributions, the deciding factor for BUS233 is the lack of the population standard deviation, sigma. Therefore, use the t-distribution.

The Excel solution is:

Rounding to two decimal places, the interval is (1.22, 3.41).

**Download the Excel workbook: Confidence-Interval-mean-when-Sigma-Not-Known**

For the StatCrunch solution, use the **Stat > T Stats > One Sample > With Data** sequence to open the dialog box.

Select the column containing the data, click on the radio button next to **Confidence Interval for ****µ**, enter the confidence level, c, and click **Compute!**

Again, we get the interval (1.22, 3.41).