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