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A **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)**.