Ti 83 for Calculating 2 Paired Sample Interval

Introduction

When you have two related samples (paired data) and want to estimate the mean difference between them with a certain level of confidence, you need to calculate a confidence interval. The TI-83 calculator can help with this through its statistical functions.

This guide covers:

• How to enter paired data into the TI-83
• The formula for calculating paired sample intervals
• Step-by-step calculator instructions
• How to interpret the results

How to Use the TI-83 for Paired Sample Intervals

Step 1: Enter Your Data

1. Press the STAT button to enter the statistics menu.
2. Use the right arrow key to move to the EDIT screen.
3. Enter your paired data in two lists (L1 and L2).
4. For example, if you have 5 pairs of measurements, enter the first values in L1 and the second values in L2.

Step 2: Calculate the Differences

1. Press STAT, then right arrow to CALC.
2. Select 1:1-Var Stats and press ENTER.
3. Enter L1 as the first list and L2 as the second list.
4. The calculator will display the mean difference (μ) and standard deviation of the differences.

Step 3: Calculate the Confidence Interval

1. Press STAT, then right arrow to TESTS.
2. Select A:2-SampTInt and press ENTER.
3. Enter the mean difference (μ), standard deviation (σ), sample size (n), and confidence level (e.g., 0.95 for 95%).
4. The calculator will display the confidence interval.

Formula Explained

The confidence interval for the mean difference (μ) between two paired samples is calculated using:

The TI-83 uses the t-distribution because the sample size is typically small, and the population standard deviation is unknown.

Worked Example

Suppose you have the following paired measurements of before and after weights for 10 patients:

Using the TI-83:

1. Enter the before weights in L1 and after weights in L2.
2. Calculate the differences (L1 - L2) and store in L3.
3. Use 1-Var Stats on L3 to find μ = -5 and σ ≈ 2.87.
4. Use 2-SampTInt with μ = -5, σ = 2.87, n = 10, and 95% confidence.
5. The calculator returns a 95% confidence interval of (-7.28, -2.72).

This means we are 95% confident that the true mean weight loss is between 2.72 and 7.28 pounds.

Interpreting Results

The confidence interval provides a range of plausible values for the true mean difference. Key points to consider:

• If the interval includes zero, the difference is not statistically significant.
• A wider interval indicates more uncertainty in the estimate.
• The confidence level (typically 95%) represents the probability that the interval contains the true mean difference.