How to Find a P-Value on Desmos (and TI-84)
There are two reliable ways to get a p-value on the Desmos calculator built into the 2027 AP Statistics exam: let a built-in test compute it, or work it out from a test statistic you already have. This guide shows both, with the TI-84 equivalents and the one decision that trips people up: which tail to use.
ttest(L) (or zproptest, chisqtest), open Hypothesis Test, type your null value, pick Left, Both or Right, and read the p-value. From a statistic instead: right tail = 1-tdist(df).cdf(t), and for a two-sided test double the smaller tail.Method 1: let Desmos run the test
- Type the procedure with your data or summary statistics, for example
ttest(25,52.1,4.8)(sample size, mean, standard deviation). Other options arezproptest(x,n)andchisqtest(col1,col2). - Open the Hypothesis Test panel that appears under the expression.
- Type your null value in the “Null hypothesis” box. It starts at 0, so if you skip this step the p-value belongs to a test of μ = 0.
- Pick the tail that matches your alternative hypothesis: Left for <, Right for >, Both for ≠. The default is Both.
- Read the p-value, the test statistic and the degrees of freedom from the shaded graph. Very small values display as “< 0.0001”, so write p < 0.0001.
Example. A sample of 25 has mean 52.1 and standard deviation 4.8. Test H₀: μ = 50 against H₊: μ > 50. Enter ttest(25,52.1,4.8), set the null to 50 and click Right: t = 2.19, df = 24, p = 0.0193. You can also type it directly: ttest(25,52.1,4.8).null(50).pright gives 0.0193. The other properties are .p (two-sided), .pleft and .score (the statistic).
TI-84: STAT ▸ TESTS ▸ T-Test, Inpt: Stats, μ₀ = 50, x̄ = 52.1, Sx = 4.8, n = 25, μ: >μ₀, Calculate. The screen shows p = 0.0193.
Method 2: from a test statistic
Use this when you already have z, t or χ² (from a formula, or from a problem that hands you the statistic), or as a backup if a test function is unavailable.
| Statistic | Right-tail p-value | Left-tail p-value | TI-84 right tail |
|---|---|---|---|
| z | 1-normaldist(0,1).cdf(z) | normaldist(0,1).cdf(z) | normalcdf(z, 1E99) |
| t | 1-tdist(df).cdf(t) | tdist(df).cdf(t) | tcdf(t, 1E99, df) |
| χ² | 1-chisqdist(df).cdf(x) | Not used | χ²cdf(x, 1E99, df) |
Two-sided tests: find the tail beyond your statistic and double it. With a positive statistic, 2*normaldist(0,1).cdf(-z) does it in one step for z, and 2*tdist(df).cdf(-t) does it for t. Chi-square tests are always right-tailed, so there is only one p-value.
Examples, all checked against the built-in tests:
- t = 1.8344 with df = 7: right tail
1-tdist(7).cdf(1.8344)= 0.0546, two-sided = 0.1092. - z = 1.6: two-sided
2*normaldist(0,1).cdf(-1.6)= 0.1096. - χ² = 4.1667 with df = 2:
1-chisqdist(2).cdf(4.1667)= 0.1245.
Which tail? Match the alternative hypothesis
| Alternative hypothesis | Tail | Desmos button | Typed property |
|---|---|---|---|
| Parameter > value | Right | Right | .pright |
| Parameter < value | Left | Left | .pleft |
| Parameter ≠ value | Both (two-sided) | Both | .p |
| Chi-square test | Right only | — | — |
What a p-value means, and what it doesn’t
The p-value is the probability of getting a result at least as extreme as yours if the null hypothesis were true. A small p-value means your result would be surprising under H₀, which is evidence against it. It is not the probability that H₀ is true.
On the free-response section, compare p to the significance level α given in the problem (often 0.05) and state the conclusion in context. For the t-test above: “Because p = 0.0193 is less than α = 0.05, we reject H₀. There is convincing evidence that the true mean is greater than 50.”
Mistakes that give the wrong p-value
- Forgetting the 1 −.
cdfreturns the area to the left. For a right-tailed test you need 1 minus that. - Forgetting to double for a two-sided test when working from a statistic.
- Leaving the null at 0 in the Desmos Hypothesis Test panel.
- Picking the tail from the data instead of the hypothesis. The alternative hypothesis sets the tail, not which way your sample came out.
- Writing p = 0. A p-value is never exactly 0. Write p < 0.0001.
To see every step of a test, including the p-value, use the confidence interval & hypothesis test calculator. For z-scores and normal areas, try the z-score calculator. All the procedures side by side are in the AP Stats calculator guide, and the cheat sheet fits on one page.
Desmos syntax tested in the College Board practice calculator and checked against independent statistical software. Updated for the May 2027 exam. Last reviewed October 2026.
Frequently Asked Questions
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How do I find a p-value on Desmos?
Type a test such as ttest, zproptest or chisqtest with your data, open the Hypothesis Test panel, enter your null value, choose Left, Both or Right to match your alternative hypothesis, and read the p-value. If you already have a test statistic, use the distribution functions instead, for example 1-tdist(df).cdf(t) for a right-tailed t-test.
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Is the Desmos p-value one-sided or two-sided?
It depends on the tail button. The Hypothesis Test panel starts on Both, which is two-sided. Choose Left or Right for a one-sided test. When typing properties, .p is two-sided, .pleft is the left tail and .pright is the right tail.
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How do I find a p-value on a TI-84?
Use STAT, TESTS and pick the matching test, such as T-Test, 1-PropZTest or the chi-square test. Choose the alternative hypothesis on the setup screen and press Calculate. From a test statistic, use tcdf(t, 1E99, df), normalcdf(z, 1E99) or the chi-square cdf function in the DISTR menu.
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What p-value counts as statistically significant on AP Statistics?
Compare the p-value with the significance level alpha given in the problem, most often 0.05. If the p-value is less than alpha, you reject the null hypothesis and state that there is convincing evidence for the alternative in the context of the problem. Otherwise you fail to reject it, which is not the same as proving it true.