Table of Contents
The TI-84 calculator can be used to calculate the margin of error of a given sample size. This calculator is able to calculate the margin of error using the t-distribution formula, which is based on the degrees of freedom and the confidence interval. The calculator will then output the margin of error for the given sample size.
Often in statistics we use to estimate the value of a 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):
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