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How to Calculate Confident Interval on Ti-84

Reviewed by Calculator Editorial Team

Calculating a confidence interval on the TI-84 calculator is essential for statistics students and professionals. This guide provides step-by-step instructions, the formula, and practical examples to help you understand and apply confidence intervals effectively.

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.

The TI-84 calculator can compute confidence intervals for means and proportions. This guide focuses on calculating a confidence interval for the mean using the TI-84.

Confidence Interval Formula

The formula for a confidence interval for the mean is:

Confidence Interval = X̄ ± (Critical Value × (σ/√n))

Where:

  • X̄ = Sample mean
  • Critical Value = Z-score or t-score from the appropriate distribution table
  • σ = Population standard deviation (if known)
  • s = Sample standard deviation (if σ is unknown)
  • n = Sample size

For large samples (n ≥ 30), you typically use the Z-distribution. For small samples, you use the t-distribution with (n-1) degrees of freedom.

Step-by-Step Guide

  1. Enter Your Data

    Press STAT, then EDIT to enter your data into the list editor. Store your data in a list (e.g., L1).

  2. Calculate Basic Statistics

    Press STAT, then CALC, then 1-Var Stats. Enter your list name (e.g., L1) and press ENTER. This will display the sample mean (X̄), sample standard deviation (s), and sample size (n).

  3. Determine the Critical Value

    For a 95% confidence interval, the critical value is approximately 1.96 for large samples. For small samples, use the t-distribution table (STAT, then TESTS, then T-Test).

  4. Calculate the Margin of Error

    Multiply the critical value by the standard error (s/√n).

  5. Compute the Confidence Interval

    Add and subtract the margin of error from the sample mean to get the confidence interval.

Worked Example

Suppose you have a sample of 20 students with an average height of 68 inches and a standard deviation of 3 inches. Calculate a 95% confidence interval for the mean height.

  1. Sample mean (X̄) = 68 inches
  2. Sample standard deviation (s) = 3 inches
  3. Sample size (n) = 20
  4. Critical value (t) ≈ 2.093 (from t-table for 19 degrees of freedom)
  5. Margin of error = t × (s/√n) = 2.093 × (3/√20) ≈ 1.24 inches
  6. Confidence interval = 68 ± 1.24 = (66.76, 69.24) inches

You can be 95% confident that the true average height of all students falls between 66.76 and 69.24 inches.

FAQ

What is the difference between a confidence interval and a confidence level?

A confidence level (e.g., 95%) is the percentage of confidence you have that the interval contains the true parameter. A confidence interval is the actual range of values calculated from your sample data.

When should I use a Z-distribution instead of a t-distribution?

Use the Z-distribution when your sample size is large (n ≥ 30) and the population standard deviation is known. For small samples or when the population standard deviation is unknown, use the t-distribution.

How do I interpret a 95% confidence interval?

A 95% confidence interval means that if you were to take 100 different samples and calculate 100 confidence intervals, approximately 95 of those intervals would contain the true population parameter.