Calculating Confidence Interval with Ti-84 with Sample N

Calculating a confidence interval with a TI-84 calculator is a common statistical task. This guide explains how to perform the calculation using your TI-84 graphing calculator, including step-by-step instructions, formulas, and practical examples.

Introduction

A confidence interval provides a range of values that is likely to contain the true population parameter with a certain level of confidence. When working with a sample size n, you can use your TI-84 calculator to compute this interval efficiently.

This guide covers:

The confidence interval formula
Step-by-step instructions for TI-84
A practical worked example
How to interpret your results

Formula

The general formula for a confidence interval for a population mean (μ) when the population standard deviation (σ) is known is:

Confidence Interval = x̄ ± z*(σ/√n)

Where:

x̄ = sample mean
z = z-score corresponding to the desired confidence level
σ = population standard deviation
n = sample size

For a 95% confidence interval, the z-score is approximately 1.96. For other confidence levels, you would use the appropriate z-score.

Steps to Calculate

Step 1: Enter Your Data

First, enter your sample data into the TI-84 calculator. You can do this by pressing STAT, then EDIT to enter your list of numbers.

Step 2: Calculate Sample Statistics

To find the sample mean (x̄) and sample standard deviation (s), follow these steps:

Press STAT, then arrow right to CALC.
Select 1:1-Var Stats.
Enter your list name (e.g., L1) and press ENTER.
Note the values for x̄ (sample mean) and s (sample standard deviation).

Step 3: Determine the Z-Score

For a 95% confidence interval, use a z-score of 1.96. For other confidence levels, you can find the appropriate z-score using the TI-84's normal distribution functions.

Step 4: Calculate the Margin of Error

Use the formula for the margin of error (ME):

ME = z*(s/√n)

Step 5: Compute the Confidence Interval

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

Lower bound = x̄ - ME

Upper bound = x̄ + ME

Worked Example

Let's calculate a 95% confidence interval for a sample with n=30, sample mean x̄=50, and sample standard deviation s=10.

Step 1: Identify Values

n = 30
x̄ = 50
s = 10
z = 1.96 (for 95% confidence)

Step 2: Calculate Margin of Error

ME = 1.96*(10/√30) ≈ 1.96*1.826 ≈ 3.56

Step 3: Compute Confidence Interval

Lower bound = 50 - 3.56 ≈ 46.44

Upper bound = 50 + 3.56 ≈ 53.56

Result

The 95% confidence interval is approximately (46.44, 53.56).

Interpreting Results

When you calculate a confidence interval, you're estimating the range where the true population parameter is likely to fall. For our example:

We're 95% confident that the true population mean falls between 46.44 and 53.56.
This means if we took many samples and calculated 95% confidence intervals for each, about 95% of those intervals would contain the true population mean.

Note: The confidence level represents the probability that the interval contains the true parameter, not the probability that the true parameter falls within a specific interval.

FAQ

What if I don't know the population standard deviation?

If you don't know the population standard deviation, you should use the sample standard deviation (s) in the formula. This approach is called a t-distribution confidence interval, which is more appropriate when σ is unknown.

How do I choose the confidence level?

The confidence level is typically chosen based on the desired level of certainty. Common choices are 90%, 95%, and 99%. Higher confidence levels result in wider intervals.

What does a wider confidence interval mean?

A wider confidence interval indicates more uncertainty about the true population parameter. This can happen with smaller sample sizes or higher confidence levels.