# How to Calculate Confidence Intervals on a TI-84 Calculator

confidence interval (C.I.) is a range of values that is likely to include a population parameter with a certain degree of confidence.

This tutorial explains how to calculate the following confidence intervals on a TI-84 calculator:

• Confidence interval for a population mean; σ known
• Confidence interval for a population mean; σ unknown
• Confidence interval for a population proportion

### Example 1: C.I. for a population mean; σ known

Find a 95% confidence interval for a population mean, given the following information:

• sample mean x = 14
• sample size n = 35
• population standard deviation = 4

Step 1: Choose Z Interval.

Press Stat and then scroll over to TESTS. Highlight 7:ZInterval and press Enter. Step 2: Fill in the necessary information.

The calculator will ask for the following information:

• Inpt: Choose whether you are working with raw data (Data) or summary statistics (Stats). In this case, we will highlight Stats and press ENTER.
• σ: The population standard deviation. We will type 4 and press  ENTER.
• x: The sample mean. We will type 14 and press  ENTER.
• n: The sample size. We will type 35 and press ENTER.
• C-level:The confidence level We will type 0.95 and press ENTER.

Lastly, highlight Calculate and press ENTER. Step 3: Interpret the results.

Once you press ENTER, the 95% confidence interval for the population mean will be displayed: The 95% confidence interval for the population mean is (12.675, 15.325).

### Example 2: C.I. for a population mean; σ unknown

Find a 95% confidence interval for a population mean, given the following information:

• sample mean x = 12
• sample size n = 19
• sample standard deviation = 6.3

Step 1: Choose T Interval.

Press Stat and then scroll over to TESTS. Highlight 8:TInterval and press Enter. Step 2: Fill in the necessary information.

The calculator will ask for the following information:

• Inpt: Choose whether you are working with raw data (Data) or summary statistics (Stats). In this case, we will highlight Stats and press ENTER.
• x: The sample mean. We will type 12 and press  ENTER.
• Sx: The sample standard deviation. We will type 6.3 and press  ENTER.
• n: The sample size. We will type 19 and press ENTER.
• C-level:The confidence level We will type 0.95 and press ENTER.

Lastly, highlight Calculate and press ENTER. Step 3: Interpret the results.

Once you press ENTER, the 95% confidence interval for the population mean will be displayed: The 95% confidence interval for the population mean is (8.9635, 15.037).

### Example 3: C.I. for a population proportion

Find a 95% confidence interval for a population proportion, given the following information:

• number of “successes” (x) = 12
• number of trials (n) = 19

Step 1: Choose 1 Proportion Z Interval.

Press Stat and then scroll over to TESTS. Highlight 1-PropZInt and press Enter. Step 2: Fill in the necessary information.

The calculator will ask for the following information:

• x: The number of successes. We will type 12 and press  ENTER.
• n: The number of trials. We will type 19 and press ENTER.
• C-level:The confidence level We will type 0.95 and press ENTER.

Lastly, highlight Calculate and press ENTER. Step 3: Interpret the results.

Once you press ENTER, the 95% confidence interval for the population proportion will be displayed: The 95% confidence interval for the population proportion is (0.41468, 0.84848).