Often in statistics we use confidence intervals to estimate the value of a population parameter with a certain level of confidence.

Every confidence interval takes on the following form:

Confidence Interval = [lower bound, upper bound]

The **margin of error** is equal to half the width of the entire confidence interval.

For example, suppose we have the following confidence interval for a population proportion:

95% confidence interval = [0.34, 0.46]

The width of the confidence interval is 0.46 – 0.34 = 0.12. The margin of error is equal to half the width, which would be 0.12 / 2 = **0.6**.

The following examples show how to calculate the margin of error for confidence intervals on a TI-84 calculator.

**Example 1: Margin of Error for a Population Mean**

Suppose you would like to calculate the margin of error for a 95% confidence interval that estimates a population mean with the following information:

**x:**30.4**s:**4.5**n:**50

To calculate the confidence interval for the population mean, press STAT and then scroll over to the right and press TESTS. Then press 7:

Next, type in the following information and then press CALCULATE:

The confidence interval turns out to be **(29.153, 31.647)**:

The margin of error would be equal to half the width of this confidence interval, which would be:

**Margin of error:** (31.647 – 29.153) / 2 = **1.247**

**Example 2: Margin of Error for a Population Proportion**

Suppose you would like to calculate the margin of error for a 95% confidence interval that estimates a population proportion with the following information:

**x:**42**n:**90

To calculate the confidence interval for the population mean, press STAT and then scroll over to the right and press TESTS. Then scroll down to press 1-PropZInt and press ENTER.

Next, type in the following information and then press CALCULATE:

The confidence interval turns out to be **(.3636, .56974)**:

The margin of error would be equal to half the width of this confidence interval, which would be:

**Margin of error:** (.56974 – .3636) / 2 = **.10307**

**Additional Resources**

How to Calculate Confidence Intervals on a TI-84 Calculator

How to Find the Z Critical Value on a TI-84 Calculator

How to Find the T Critical Value on a TI-84 Calculator

There’s a typo above. It says “0.12 / 2 = 0.6”. Of course it’s actually 0.06. Typos aside, I really like the way you explain things!