How to run a t-test on the TI-84 and read the output

Where the t-test lives on the TI-84

Every inference procedure on a TI-84 sits behind one key. Press STAT, arrow right twice to the TESTS tab, and scroll the list of procedures by name. Choose T-Test when you have one sample and a claim about a population mean $\mu$ (mu), and 2-SampTTest when you have two independent samples.

The t procedures are the right family whenever the population standard deviation $\sigma$ (sigma) is unknown, which is almost always true with real data. If a problem hands you $\sigma$ outright, the z procedures on the same menu apply instead. The guide on t-test vs z-test sorts out that choice.

The wording below is TI-84 wording, but the statistics do not depend on the device. Menu names and key sequences vary between calculators; the inputs each test needs and the meaning of each output line do not.

Data or Stats: the input choice that trips people up

The first line of the T-Test screen is Inpt, with two options, Data and Stats. Highlight one, press ENTER, then fill in the fields that appear underneath.

Choose Data when the raw values are already typed into a list. The screen asks for $\mu_0$ (mu-nought, the hypothesized mean from the null hypothesis), the List holding your values (usually L1), and Freq (leave it at 1 unless you have a separate column of counts). The calculator computes the sample mean and sample standard deviation from the list for you.

Choose Stats when the problem gives you summary numbers instead of raw data. The screen then asks for $\mu_0$, $\bar{x}$ (x-bar, the sample mean), $\text{Sx}$ (the sample standard deviation), and $n$ (the sample size).

The last two lines are identical either way. Set $\mu$ to $\ne \mu_0$, $< \mu_0$, or $> \mu_0$ so it matches your alternative hypothesis, then highlight Calculate and press ENTER. Draw returns the same numbers with the tail area shaded on a picture of the t-distribution.

What every line of the output means

Calculate returns a short results screen. Here is the one-sample T-Test output, line by line.

• The alternative hypothesis, echoed at the top, for example $\mu \ne 50$. Read this first, because a wrong tail choice changes the p-value while leaving every other line untouched.
• $t$, the test statistic. It counts how many standard errors separate your sample mean from the hypothesized mean: $t = \frac{\bar{x} - \mu_0}{\text{Sx}/\sqrt{n}}$.
• $p$, the p-value. This is the probability of a sample result at least as extreme as yours when the null hypothesis is true. It is not a sample proportion or a population proportion, so never report it as the proportion of anything in your data.
• $\bar{x}$, the sample mean, echoed back from your list or your typed input.
• $\text{Sx}$, the sample standard deviation, the version that divides by $n - 1$.
• $n$, the sample size.

The one-sample screen does not print a degrees of freedom line, and you still have to report one. For a one-sample t-test, $df = n - 1$, so a sample of 25 gives $df = 24$. Work it out and write it down.

Watch for scientific notation in the p-value. A display of 3.2E-4 means 0.00032, a very small p-value rather than a large one. For output across the other procedures, see reading calculator output.

Two independent samples with 2-SampTTest

2-SampTTest compares the means of two groups made of different individuals, such as a treatment group and a control group. Under Data it asks for List1 and List2. Under Stats it asks for $\bar{x}_1$, $\text{Sx1}$, $n_1$, then $\bar{x}_2$, $\text{Sx2}$, $n_2$.

Two prompts appear that the one-sample screen does not have. Set $\mu_1$ to $\ne \mu_2$, $< \mu_2$, or $> \mu_2$ for your alternative. Then answer Pooled, which asks whether to merge the two sample standard deviations into a single estimate; leave it on No unless a problem states that the population variances are equal. The guide on pooling or not on a two-sample t-test explains why No is the safe default.

The output is longer. You get the alternative, $t$, $p$, $df$, then $\bar{x}_1$, $\bar{x}_2$, $\text{Sx1}$, $\text{Sx2}$, $n_1$, and $n_2$, so scroll to the bottom before you copy anything. This screen does print $df$, and it will not be a whole number.

Why the two-sample df comes back as a decimal

A one-sample df is a count, $n - 1$. A two-sample df is an approximation, so the calculator returns something like 24.2267 instead of a tidy integer. Nothing is broken. The TI-84 uses the Welch approximation, which weights each sample variance by its own sample size:

Try it with $n_1 = 12$, $s_1 = 5.2$, $n_2 = 15$, and $s_2 = 7.9$. Then $\frac{s_1^2}{n_1} = \frac{27.04}{12} = 2.2533$ and $\frac{s_2^2}{n_2} = \frac{62.41}{15} = 4.1607$, so the numerator is $6.414^2 = 41.1394$ and the denominator is $\frac{2.2533^2}{11} + \frac{4.1607^2}{14} = 0.4616 + 1.2365 = 1.6981$. Dividing gives $df = \frac{41.1394}{1.6981} = 24.2267$.

The AP course states that the two-sample degrees of freedom fall between the smaller of $n_1 - 1$ and $n_2 - 1$ and the value $n_1 + n_2 - 2$, and that technology finds them. Here that range runs from 11 to 25, and 24.2267 sits inside it. Report the decimal exactly as the screen gives it, and see why df is a decimal on a two-sample t-test for the full story.

Paired data is a one-sample T-Test on the differences

This is the most common TI-84 error in an AP Statistics classroom. When each value in one group is matched to a specific value in the other, such as a before and after measurement on the same person, the two samples are not independent. Running 2-SampTTest on that data throws the pairing away and usually understates the evidence.

The fix takes three moves. Press STAT, choose EDIT, and put the first measurement in L1 with each matched second measurement beside it in L2. Arrow up onto the L3 column header, type L2 - L1 (the list names are 2nd then 2, and 2nd then 1), and press ENTER to fill L3 with the differences.

Now run T-Test on L3 with Inpt: Data, List: L3, and $\mu_0 = 0$. You are testing a claim about $\mu_d$ (mu-d, the population mean difference), and $df = n - 1$ where $n$ counts the pairs, not the individual measurements. The AP course puts it the same way: for a matched pairs design with two dependent samples, you calculate differences between pairs to produce one sample of differences, and the procedure is a one-sample t-test for the population mean difference.

Decide your order of subtraction before you start, since it fixes the sign of $t$ and the direction of a one-sided alternative. The paired vs two-sample t-test comparison shows how to tell the two designs apart from the wording of a problem.

What to write down after you press Calculate

The screen is a source of numbers, not a finished answer. Copy the test statistic, the degrees of freedom, and the p-value, then write a conclusion in your own words. A bare menu name with no numbers beside it does not show any reasoning.

Round the statistic to two or three decimals and keep the p-value to three or four. Compare that p-value to your significance level $\alpha$ (alpha, the cutoff you chose in advance, usually 0.05), then say what the decision means for the original question rather than only for $H_0$, the null hypothesis.

Before you trust any output, check the echoed $\bar{x}$, $\text{Sx}$, and $n$ against your data. A single mistyped value shows up on those lines immediately. If you have raw data and want those summary numbers on their own, 1-Var Stats reports x-bar and Sx without running a test at all.

How this fits the Fall 2026 AP course

A graphing calculator with statistical capabilities is expected on both sections of the AP Statistics exam that takes effect in Fall 2026, with the first exam in May 2027. Formulas and tables are provided, so the work on exam day is choosing the right procedure and reading its output, not recalling critical values.

One-sample and matched pairs t-tests are Unit 4 topics 4.4 and 4.5, Setting Up and Carrying Out a Test for a Population Mean or Population Mean Difference. Two independent samples are topics 4.9 and 4.10. Unit 4, Inference for Quantitative Data: Means, carries 10 to 20 percent of the multiple-choice section, and free-response Question 3 is an inference question every year.

Conditions still come before the calculator. A one-sample t procedure needs data from a random sample or a randomized experiment, the 10 percent condition when sampling without replacement, and either an approximately normal population, $n \ge 30$, or sample data free from strong skewness and outliers. For matched pairs, that count applies to the number of differences, not the number of measurements.