A confidence interval is a range of values that is likely to contain a population parameter with a certain level of confidence. It can be used to estimate unknown population characteristics, such as the mean, the proportion, the standard deviation, and more.
The TI-84 calculator has a built-in function that can compute confidence intervals for you, as long as you have the appropriate sample statistics and the confidence level. In this article, we will show you how to use the confidence interval function on a TI-84 calculator, and provide some examples and tips along the way.
How to Access the Confidence Interval Function
The confidence interval function can be accessed on a TI-84 calculator by following these steps:
- Press the STAT key and then press the right-arrow key to move to the TESTS menu.
- Scroll down to the option that corresponds to the type of confidence interval you want to find. There are several options available, such as:
- 1:ZInterval for a confidence interval for a population mean when the population standard deviation is known
- 2:TInterval for a confidence interval for a population mean when the population standard deviation is unknown
- 3:2-SampZInt for a confidence interval for the difference between two population means when the population standard deviations are known
- 4:2-SampTInt for a confidence interval for the difference between two population means when the population standard deviations are unknown
- 5:1-PropZInt for a confidence interval for a population proportion
- 6:2-PropZInt for a confidence interval for the difference between two population proportions
- 7:ZInterval for a confidence interval for a population standard deviation
- 8:TInterval for a confidence interval for a population variance
- Press ENTER to select the option you want. This will bring up the confidence interval function on the screen.
How to Use the Confidence Interval Function
The confidence interval function has different syntaxes depending on the type of confidence interval you want to find. However, they all have some common arguments, such as:
- Inpt: Choose whether you are working with raw data (Data) or summary statistics (Stats). If you choose Data, you will need to enter the lists of values for the variables. If you choose Stats, you will need to enter the sample statistics, such as the mean, the standard deviation, the proportion, etc.
- C-Level: The confidence level, which is a number between 0 and 1 that represents the degree of confidence you have in the interval. For example, a 95% confidence level means that you are 95% confident that the interval contains the true population parameter.
- Calculate: Choose this option to compute the confidence interval and display the results on the screen.
- Draw: Choose this option to draw the confidence interval on a graph.
Examples of Using the Confidence Interval Function
Let’s look at some examples of how to use the confidence interval function on a TI-84 calculator.
Example 1: Confidence Interval for a Population Mean; σ Known
Question: A random sample of 50 students has a mean GPA of 3.2 and a population standard deviation of 0.5. Find a 90% confidence interval for the population mean GPA.
Answer: To find the confidence interval, we need to use the ZInterval function with the following arguments:
- Inpt: Stats
- σ: 0.5
- x: 3.2
- n: 50
- C-Level: 0.9
Press STAT and then scroll right to the TESTS menu. Scroll down to option 1:ZInterval and press ENTER. For Inpt, highlight Stats and press ENTER. For σ, type 0.5 and press ENTER. For x, type 3.2 and press ENTER. For n, type 50 and press ENTER. For C-Level, type 0.9 and press ENTER. Scroll down to Calculate and press ENTER. On the new screen, we can see the output of the ZInterval function:
From the output, we can see that the 90% confidence interval for the population mean GPA is (3.068, 3.332).
Example 2: Confidence Interval for a Population Proportion
Question: In a survey of 200 voters, 120 said they would vote for candidate A. Find a 95% confidence interval for the population proportion of voters who would vote for candidate A.
Answer: To find the confidence interval, we need to use the 1-PropZInt function with the following arguments:
- Inpt: Stats
- x: 120
- n: 200
- C-Level: 0.95
Press STAT and then scroll right to the TESTS menu. Scroll down to option 5:1-PropZInt and press ENTER. For Inpt, highlight Stats and press ENTER. For x, type 120 and press ENTER. For n, type 200 and press ENTER. For C-Level, type 0.95 and press ENTER. Scroll down to Calculate and press ENTER. On the new screen, we can see the output of the 1-PropZInt function:
From the output, we can see that the 95% confidence interval for the population proportion of voters who would vote for candidate A is (0.516, 0.684).
Tips and Tricks for Using the Confidence Interval Function
Here are some tips and tricks for using the confidence interval function on a TI-84 calculator:
- To enter the lists of values for the variables, press STAT and then press EDIT. Enter the values in the columns L1, L2, etc. To name the lists, press 2nd and then press STAT. Scroll down to the list you want to name and press ENTER. Type the name and press ENTER.
- To enter the sample statistics for the variables, press STAT and then press the right-arrow key to move to the TESTS menu. Scroll down to the option you want and press ENTER. For Inpt, highlight Stats and press ENTER. Enter the values for the sample statistics, such as the mean, the standard deviation, the proportion, etc.
- To enter the confidence level, you can use any number between 0 and 1 that represents the degree of confidence you have in the interval. For example, a 95% confidence level means that you are 95% confident that the interval contains the true population parameter. To enter the confidence level, type the decimal equivalent of the percentage. For example, to enter a 95% confidence level, type 0.95.
- To draw the confidence interval on a graph, press STAT and then scroll right to the TESTS menu. Scroll down to the option you want and press ENTER. Enter the arguments for the confidence interval function. Scroll down to Draw and press ENTER. The calculator will display the graph of the confidence interval, along with the lower and upper bounds of the interval.