How to Calculate Confidence Interval with Ti 84

Introduction

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. For example, if you calculate a 95% confidence interval for the mean height of students in a school, you can be 95% confident that the true average height falls within that range.

The TI-84 calculator provides built-in functions to calculate confidence intervals for means and proportions. This guide will focus on calculating confidence intervals for means, which is the most common application.

Prerequisites

Before you begin, you should have:

• A TI-84 calculator (TI-84 Plus or TI-84 Plus CE)
• A sample of data points
• Knowledge of basic statistics (mean, standard deviation)

If you're not familiar with these concepts, you may want to review basic statistics before proceeding.

Step-by-Step Guide

Follow these steps to calculate a confidence interval for the mean using your TI-84 calculator:

Step 1: Enter Your Data

First, you need to enter your data into the calculator. Here's how:

1. Press the STAT button
2. Select Edit (L1 or L2)
3. Enter your data points, pressing ENTER after each one
4. Press STAT again to exit the edit mode

Step 2: Calculate Basic Statistics

Before calculating the confidence interval, you need to know the sample mean and standard deviation:

1. Press STAT then select CALC
2. Select 1-Var Stats (L1 or L2)
3. Enter the list name (e.g., L1) and press ENTER
4. Note the values for x̄ (sample mean) and Sx (sample standard deviation)

Step 3: Calculate the Confidence Interval

Now you're ready to calculate the confidence interval:

1. Press STAT then select TESTS
2. Select A:1-PropZInt or B:2-PropZInt depending on your data type
3. For a confidence interval for the mean, select B:2-PropZInt
4. Enter the following values:
   • x̄: Sample mean
   • Sx: Sample standard deviation
   • n: Sample size
   • C-Level: Confidence level (e.g., 0.95 for 95%)
5. Press ENTER to calculate

Step 4: Interpret the Results

The calculator will display the confidence interval in the format "Lower Bound, Upper Bound". For example, "12.3, 18.7" would indicate a 95% confidence interval of 12.3 to 18.7.

This means you can be 95% confident that the true population mean falls within this range.

Worked Example

Let's walk through a complete example to calculate a 95% confidence interval for the mean height of students in a school.

Sample Data

Suppose we have the following sample of student heights (in inches):

Step 1: Enter Data

Enter these values into your TI-84 calculator in list L1.

Step 2: Calculate Basic Statistics

Using the 1-Var Stats function, you'll find:

• Sample mean (x̄) = 66.8 inches
• Sample standard deviation (Sx) ≈ 2.96 inches
• Sample size (n) = 10

Step 3: Calculate Confidence Interval

Using the 2-PropZInt function with a 95% confidence level (C-Level = 0.95), the calculator will return:

Confidence Interval: (65.2, 68.4)

Interpretation

We can be 95% confident that the true average height of all students in the school falls between 65.2 and 68.4 inches.

Interpreting Results

When you calculate a confidence interval, it's important to understand what the result means:

• The confidence interval provides a range of values that is likely to contain the true population parameter
• The confidence level (e.g., 95%) represents the probability that the interval contains the true parameter
• A narrower interval indicates more precise estimates, while a wider interval suggests more uncertainty

Common confidence levels are 90%, 95%, and 99%. Higher confidence levels result in wider intervals, while lower confidence levels produce narrower intervals.