T-Test and Z-Test on TI-84: Step-by-Step for AP Stats

Hypothesis tests for a population mean are a huge part of AP Statistics — and the TI-84 does the heavy arithmetic for you. This guide covers the t-test on TI-84 step by step, plus when to use a z-test instead and how to read the output like a pro.

T-Test or Z-Test: Which One?

• T-Test — use when the population standard deviation (σ) is unknown, which is almost always in AP Stats. You’ll estimate it from your sample.
• Z-Test — use only when the population standard deviation (σ) is known. Rare in practice, but it shows up in textbook problems.

When in doubt on the AP exam: T-Test. The button sequences below are identical for both — only the menu choice differs.

Step 1: Enter Your Data

1. Press STAT, then 1 (Edit).
2. Clear L1 if needed: highlight L1, press CLEAR, then ENTER.
3. Type your sample values into L1, pressing ENTER after each.

(If the problem gives you summary statistics — sample mean, standard deviation, and n — instead of raw data, you can skip this and choose “Stats” input in Step 3.)

Step 2: Open the Test Menu

Press STAT, arrow right to TESTS, and select:

• 2: T-Test… for a t-test, or
• 1: Z-Test… for a z-test (σ known).

Step 3: Fill In the Settings

• Inpt: choose Data (you entered raw data) or Stats (you have summary statistics).
• μ0: the hypothesized population mean from H0 (the “equals” value).
• List: L1 (if Data input). Freq: 1.
• μ: highlight your alternative hypothesis — ≠μ0, <μ0, or >μ0. Match it to Ha exactly.
• Arrow down to Calculate and press ENTER. (Choose Draw instead if you want the t-curve with the p-value shaded — great for checking your understanding.)

Step 4: Read the Output

The calculator shows:

• t = (or z =): your test statistic — how many standard errors the sample mean is from μ0.
• p =: the p-value.
• x̄ =, sx =, n =: your sample statistics (confirmation you entered data correctly).

The decision rule: if p < α (your significance level, often 0.05), reject H0. If p ≥ α, fail to reject H0. That’s the entire conclusion — the calculator handed you the key number.

Worked Mini-Example

A sample of 25 students has x̄ = 78, s = 6. Test H0: μ = 75 vs. Ha: μ > 75 at α = 0.05.

1. STAT → TESTS → 2: T-Test.
2. Inpt: Stats, x̄: 78, sx: 6, n: 25, μ0: 75, μ: >μ0.
3. Calculate → t = 2.5, p = 0.0098.
4. Since 0.0098 < 0.05, reject H0 — convincing evidence the mean exceeds 75.

Common Mistakes to Avoid

• Picking Z-Test with unknown σ: the #1 error. Unless the problem explicitly gives you the population σ, it’s a t-test.
• Wrong alternative hypothesis direction: a two-sided Ha (≠) when the question asks “greater than” doubles your p-value and flips your conclusion. Read the question’s wording carefully.
• Data in the wrong list: if you stored data in L2 but the test reads L1, your results are nonsense. Double-check the List setting.
• Confusing p with α: the calculator gives you p; α comes from the problem (default 0.05 if unstated). Compare them — don’t mix them up.

Frequently Asked Questions

How do I do a t-test on TI-84? Press STAT → TESTS → 2: T-Test. Enter μ0, choose Data or Stats, set the alternative hypothesis (≠, <, >), and select Calculate. Read the p-value from the output.

When should I use a z-test instead of a t-test? Only when the population standard deviation σ is known. In AP Statistics that’s rare — default to the t-test.

What does the p-value tell me? It’s the probability of getting a sample as extreme as yours (or more) if H0 were true. Small p (below α) means your data is surprising under H0 — reject it.

What’s the difference between Calculate and Draw? Calculate gives you the numbers; Draw also graphs the distribution with the p-value area shaded. Same results — Draw just helps you visualize.

Run One Yourself

Follow the mini-example above on our free online TI-84 Plus CE at https://freeti84calculator.com/ — no download needed. More AP Statistics step-by-steps are in the guides hub at https://freeti84calculator.com/guides/.