How To Do A Paired T Test On Ti 84

How to do a paired t test on TI‑84 is a step‑by‑step process that the calculator simplifies, allowing you to compare the means of two related samples with just a few keystrokes. This guide walks you through every stage—from preparing your data to interpreting the output—so you can complete the test confidently and accurately, whether you are a high‑school student, a college freshman, or a self‑learner brushing up on statistics Not complicated — just consistent..

What Is a Paired t Test?

A paired t test evaluates whether the average difference between two sets of related observations is significantly different from zero. Even so, Typical examples include before‑and‑after measurements on the same subjects, matched‑pair experiments, or repeated measures. The test assumes that the differences are approximately normally distributed and that the data are continuous Not complicated — just consistent. That's the whole idea..

Real talk — this step gets skipped all the time.

Why Use the TI‑84?

The TI‑84 graphing calculator includes built‑in statistical functions that let you perform a paired t test without needing external software. Its intuitive menu system makes it accessible for beginners, while its precision ensures reliable results for academic projects and quick analyses Worth keeping that in mind. Simple as that..

Quick note before moving on.

Step‑by‑Step Guide to Enter Data

1. Create a new list

   • Press STAT → EDIT.
   • Select an empty list (e.g., L1) and enter the first set of paired values.
   • Move to the next column and enter the second set of values into L2.

2. Check your entries

   • Verify that each pair occupies the same row in L1 and L2.
   • Ensure there are no missing or extra values, as mismatched lengths will cause an error.

3. Name the lists (optional)

   • While still in EDIT, press 2ND → 0 (catalog).
   • Scroll to the list you are using, press ENTER, then type a short name (e.g., BEFORE) and press ENTER again.
   • Repeat for the second list (e.g., AFTER). Naming lists helps keep your work organized.

Running the Paired t Test on the TI‑84

1. Access the test menu

   • Press STAT → scroll right to the TESTS menu.
   • Choose 2:T-Test.

2. Select “Paired”

   • Highlight Paired and press ENTER.
   • The calculator will prompt you for the two data lists.

3. Enter the list names

   • For μ₁: type the name of the first list (e.g., BEFORE).
   • For μ₂: type the name of the second list (e.g., AFTER).
   • Leave μ₀ (the hypothesized mean difference) at 0 unless your problem specifies otherwise

3. Choose the Alternative Hypothesis

The calculator asks for the alternative hypothesis (μ₁ – μ₂). Use the arrow keys to highlight one of the three options and press ENTER:

If the problem states a direction (e.g., “the new drug lowers blood pressure”), select the appropriate one; otherwise keep the default ≠ μ₀.

4. Run the Test

After you’ve entered the list names, the calculator will automatically fill in the sample sizes (n₁ and n₂). Press ENTER to move to the next line, then ENTER again to execute the test.

The calculator displays a results screen similar to:

t = 2.34
p = 0.023
μ₁ = 12.5
μ₂ = 10.8
sd = 3.42
n = 15

• t – the test statistic.
• p – the p‑value (probability of observing a difference at least as extreme if the null hypothesis is true).
• μ₁ and μ₂ – the sample means of the two lists.
• sd – the standard deviation of the paired differences.
• n – number of pairs.

5. Interpret the Output

1. Decision Rule

   • Choose an alpha level (commonly α = 0.05).
   • If p < α, reject the null hypothesis (H₀: μ₁ – μ₂ = 0).
   • If p ≥ α, fail to reject H₀.

2. Practical Meaning

   • Rejecting H₀ means there is statistically significant evidence that the mean difference between the paired observations is not zero.
   • Failing to reject H₀ suggests the observed difference could be due to random sampling variation.

3. Direction (for one‑tailed tests)

   • When you selected > or <, also verify that the sign of the t statistic aligns with your expectation (e.g., a positive t supports a claim that μ₁ > μ₂).

6. (Optional) Compute a Confidence Interval for the Mean Difference

A paired t test often accompanies a confidence interval (CI) to show the plausible range of the true mean difference. To obtain it:

1. Return to the TESTS menu (STAT → ►TESTS).
2. Choose 7:InvT (inverse t) or use 0:ClrList? Actually the TI‑84’s built‑in CI for paired data is accessed via STAT → TESTS → 0:2‑PropZTest? No, for paired t you can use STAT → TESTS → 2:T‑Test again but this time select ≠ μ₀ and then press ENTER to get the CI automatically displayed after the test results.
   • Alternatively, use STAT → CALC → 7:TInterval.
   • Set Data option, enter the list of differences (you can store them in a temporary list: L3 = L1 – L2).
   • Set the confidence level (e.g., 95%).

The calculator will output something like:

(0.45, 2.87)

indicating that we are 95 % confident the true mean difference lies between 0.45 and 2.87 units The details matter here. Turns out it matters..

7. Tips, Common Pitfalls, and Quick Checks

8. Additional Tips and Troubleshooting

Quick Checklist Before Running the Paired t Test

1. Data Entry – Verify that L₁ and L₂ contain the same number of entries.
2. List Order – Ensure the pairs are correctly aligned (i.e., the first element of L₁ corresponds to the first element of L₂).
3. Temporary Differences – If you plan to compute a confidence interval, create the difference list (L₃ = L₁ – L₂) and clear any old data from L₃.
4. Hypothesis Selection – Choose the appropriate alternative (≠ μ₀, > μ₀, or < μ₀) based on your research question.
5. Alpha Level – Set α (usually 0.05) in the calculator’s T‑Test settings if you need to compare the p‑value manually.