How to Find a Confidence Interval for a Mean (Unknown Population Standard Deviation)

In elementary stats, you’ll often be asked to find a confidence interval for a given confidence level. If the sample if large enough (greater or equal to 30), you can use the the sample standard deviation, sx instead of the population standard deviation, σ (if you know σ, you can use a z-distribution instead). The TI-89 can answer this problem in the push of a button: all you have to do is enter the data.

Sample problem: A random sample of 30 students at a Florida college has the following grade point averages: 59.1, 65.0, 75.1, 79.2, 95.0, 99.8, 89.1, 65.2, 41.9, 55.2, 94.8, 84.1, 83.2, 74.0, 75.1, 76.2, 79.1, 80.1, 92.1, 74.2, 59.2, 64.0, 75.1, 78.2, 95.0, 97.8, 89.1, 64.2, 41.8, 57.2. What is the 90% confidence interval for the population mean?

Step 1: Press . Scroll to the Stats/List Editor and press .

Step 2: Press to clear the editor.

Step 3: Press to name the list “CI.”

Step 4: Enter your data in a list. Follow each number with the key: 59.1, 65.0, 75.1, 79.2, 95.0, 99.8, 89.1, 65.2, 41.9, 55.2, 94.8, 84.1, 83.2, 74.0, 75.1, 76.2, 79.1, 80.1, 92.1, 74.2, 59.2, 64.0, 75.1, 78.2, 95.0, 97.8, 89.1, 64.2, 41.8, 57.2.

Step 5: Press , .

Step 6: Enter “ci” in the List box: .

Step 7: Enter in the frequency box. Press . This should give you the sample standard deviation, sx = 15.6259, n = 30, and x (the sample mean) = 75.033.

Step 8: Press . Press .

Step 9: Press the right arrow key then the down arrow to select a “Data Input Method” of “Stats.” Press .

Step 10: Enter your x, sx and n from Step 7. In our example, sx = 15.6259. n = 30 and x = 75.033.

Enter the Confidence Interval from the question (in our example, it’s .9).

Step 11: Press and read the results. The C Int is {70.19,79.88} which means that we are 90% confident that the population mean falls between 70.19 and 79.88.

That’s it!

Tip: If you know σ, use ZInterval instead of TInterval.