How to Calculate Confidence Interval on 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, you can be 95% confident that the true average height falls within that range.

Your TI-84 calculator can compute confidence intervals for means, proportions, and other statistics. This guide focuses on calculating confidence intervals for means, which is the most common application.

Prerequisites

Before you begin, you'll need:

• A TI-84 calculator (TI-84 Plus or TI-84 Plus CE recommended)
• Sample data (a list of numbers you want to analyze)
• Basic understanding of statistics concepts

If you're new to statistics, you may want to review concepts like sample means, standard deviations, and the Central Limit Theorem before proceeding.

Step-by-Step Guide

Step 1: Enter Your Data

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

1. Press the STAT button to access the statistics menu
2. Select EDIT to enter data
3. Choose a list (L1, L2, etc.) to store your data
4. Enter your numbers one by one, pressing ENTER after each number

Step 2: Calculate Basic Statistics

Before calculating the confidence interval, you'll need some basic statistics:

1. Press STAT then CALC
2. Select 1-Var Stats (for one-variable statistics)
3. Enter your list name (e.g., L1)
4. Press ENTER to see the results

Note down the sample mean (x̄) and sample standard deviation (s).

Step 3: Calculate the Confidence Interval

Now you're ready to calculate the confidence interval:

1. Press STAT then TESTS
2. Select A:1-PropZInt for proportions or B:1-SampZInt for means
3. For means:
   • Enter your sample mean (x̄)
   • Enter your sample standard deviation (s)
   • Enter your sample size (n)
   • Enter your confidence level (e.g., 0.95 for 95%)
4. Press ENTER to see the confidence interval

Step 4: Interpret the Results

The calculator will display two numbers: the lower bound and upper bound of your confidence interval. For example, if you get (4.2, 6.8), this means you're 95% confident that the true population mean falls between 4.2 and 6.8.

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 you measure the heights (in inches) of 20 randomly selected students:

62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82

Step 1: Enter Data

Enter these numbers into list L1 on your calculator.

Step 2: Calculate Basic Statistics

Using 1-Var Stats, you'll find:

• Sample mean (x̄) = 71.55 inches
• Sample standard deviation (s) ≈ 6.25 inches
• Sample size (n) = 20

Step 3: Calculate Confidence Interval

Using the calculator's 1-SampZInt function with a 95% confidence level (z ≈ 1.96):

Lower bound = 71.55 - (1.96 * 6.25 / √20) ≈ 69.26

Upper bound = 71.55 + (1.96 * 6.25 / √20) ≈ 73.84

Result

The 95% confidence interval for the mean height is approximately (69.26, 73.84) inches.

This means we're 95% confident that the true average height of all students in the school falls between 69.26 and 73.84 inches.

Interpreting Results

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

• The confidence level (e.g., 95%) represents the probability that the interval contains the true population parameter if you were to take many samples and calculate intervals from each.
• A 95% confidence interval means there's a 5% chance the interval doesn't contain the true value.
• The width of the interval depends on:
  • Sample size (larger samples give narrower intervals)
  • Variability in the data (more variable data gives wider intervals)
  • Confidence level (higher confidence levels give wider intervals)