In **elementary statistics**, you’ll may have to find a CI (confidence interval) for a given confidence level such as 90% or 95%. The **TI-89 graphing calculator** is a powerful calculator that can help you answer these types of problem (that are tedious and prone to error if done by hand) in the push of a button.

Sample problem #1 (known standard deviation): Fifty students at a Florida college have the following grade point averages: 94.8, 84.1, 83.2, 74.0, 75.1, 76.2, 79.1, 80.1, 92.1, 74.2, 64.2, 41.8, 57.2, 59.1, 65.0, 75.1, 79.2, 95.0, 99.8, 89.1, 59.2, 64.0, 75.1, 78.2, 95.0, 97.8, 89.1, 65.2, 41.9, 55.2. Find the 95% confidence interval for the population mean, given that σ = 2.27.

**Step 1:** Press Apps and scroll to **Stats/List Editor**. Press Enter.

**Step 2:** Press F1 8. This clears the list editor.

**Step 3:** Press Alpha ) Alpha 9 2 to name the list “CI2.”

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

**Step 5:** Press F4, 1.

**Step 6:** Enter “ci” in the “List” box: Alpha ) Alpha 9.

**Step 7:** Enter 1 in the **frequency** box. Press Enter. This should give you the mean (xbar, the first in the list) = **75.033**.

**Step 8:** Press Enter. Press 2nd F7 1 Enter. This brings up the z-distribution menu.

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

**Step 10:** Enter your σ from the question (in our case, 2.27), xbar from Step 7 (75.3033), n = 30 and the Confidence Interval from the question (in our example, it’s .95).

**Step 11:** Press Enter and read the results. The “C Int” is **{74.49,76.123}**. This means we are 95% confident that the population mean falls between 74.49 and 76.123.

That’s it!

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, s_{x} 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 #2 (unknown standard deviation): 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 Apps. Scroll to the **Stats/List Editor** and press Enter.

**Step 2:** Press F1 8 to clear the editor.

**Step 3:** Press Alpha ) Alpha 9 to name the list “CI.”

**Step 4:** Enter your data in a list. Follow each number with the Enter 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 F4, 1.

**Step 6:** Enter “ci” in the **List** box: Alpha ) Alpha 9.

**Step 7:** Enter 1 in the **frequency** box. Press Enter. This should give you the sample standard deviation, s_{x} = 15.6259, n = 30, and x (the sample mean) = 75.033.

**Step 8:** Press Enter. Press 2nd F2 2.

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

**Step 10:** Enter your x, s_{x} and n from Step 7. In our example, s_{x} = 15.6259. n = 30 and x = 75.033.

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

**Step 11:** Press Enter 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.

Thank you very much.

My textbook is entirely geared towards TI-83, so sometimes I am left behind. But this website makes it easier to do the same thing on my more powerful calculator – in an even faster way.

Two comments to make this guide easier to understand:

1. State the displayed name for the buttons pressed such as step 8 should read “Press Enter. Press 2nd F7 1 Enter (displayed as ‘Zinterval…’). This brings up the z-distribution menu.”

That is not necessary, but it makes it more obvious what each step that gives calculator advice is telling us to do.

2. This should also have directions that tell us that we can skip steps 1-7 if we have already found (or are told) the mean of the sample given.

This information was surprisingly difficult to find, so I really appreciate that I could find it here.

Luke,

Thanks for the tip. I’ll consider that in future posts.

Regards,

Stephanie

Hi! Can you solve this manually? i mean step-by-step..tq

Try this:

Find a Confidence Interval for a Sample

Stephanie