Calculator TI-84 Quick Reference | Statistics II | VUB | 2025/26

JANUARY 1, 2026




STATISTICS II
TI-84 QUICK REFERENCE


KOEN HANEGREEFS
VUB

,Statistics II — TI-84 Quick Reference
Theory · formulas · how to enter them on the TI-84 Plus
Throughout: 1E99 means ∞ (type 1, then 2nd , for E, then 99). The two menus you live in are
DISTR (2nd VARS) for probabilities/critical values and STAT ▸ TESTS for full tests and intervals.

0. The DISTR menu (2nd VARS) — probabilities & critical values
Command What it gives Syntax
normalcdf Area / p-value under a Normal curve normalcdf(low, high[, μ,
σ])
invNorm z* from a left-tail area invNorm(area_left[, μ, σ])
invT t* from a left-tail area invT(area_left, df)
tcdf p-value from a t statistic tcdf(low, high, df)
χ²cdf p-value from a χ² statistic χ²cdf(low, high, df)
Tails: upper (t, 1E99, df) · lower (-1E99, t, df) · two-sided 2 × tcdf(|t|, 1E99, df).

Means
1. One-sample t (Ch. 11–13)
Use when: one quantitative sample, σ unknown, nearly Normal or large n. df = n − 1.
Formula TI-84
t = (ȳ − μ₀) / (s/√n) STAT ▸ TESTS ▸ 2:T-Test
CI: ȳ ± t* · (s/√n) STAT ▸ TESTS ▸ 8:TInterval
t* = invT(area_left, n−1) Input: Data (a list) or Stats (ȳ, s, n)


2. One-proportion z (Ch. 12)
Use when: one categorical (yes/no) sample. Check np₀ ≥ 10 and nq₀ ≥ 10.
Formula TI-84
z = (p̂ − p₀) / √(p₀q₀/n) STAT ▸ TESTS ▸ 5:1-PropZTest
CI: p̂ ± z* · √(p̂q̂/n) STAT ▸ TESTS ▸ A:1-PropZInt
(test uses p₀; CI uses p̂) Enter x = successes (a whole number) and n


3. Two independent means (Ch. 14)
Use when: two separate groups. Welch is the default; df comes from the calculator.
Formula TI-84
t = (ȳ₁ − ȳ₂) / √(s₁²/n₁ + s₂²/n₂) STAT ▸ TESTS ▸ 4:2-SampTTest
CI: (ȳ₁ − ȳ₂) ± t* · SE STAT ▸ TESTS ▸ 0:2-SampTInt
Welch SE = √(s₁²/n₁ + s₂²/n₂) Pooled: No = Welch · Pooled: Yes = equal-
variance

, 4. Paired means (Ch. 13)
Use when: each unit measured twice (before/after, matched). Work on the differences d. df = n −
1.
Formula TI-84
d = y₁ − y₂ for each pair Highlight L3 header, type L1 - L2, ENTER
t = d̄ / (s_d/√n) STAT ▸ TESTS ▸ 2:T-Test on L3, μ₀ = 0
CI: d̄ ± t* · (s_d/√n) (no built-in paired test — use the difference
list)


5. Two proportions (Ch. 14)
Use when: two groups, categorical response. Test pools p̂; CI does not.
Formula TI-84
z = (p̂₁ − p̂₂) / √(p̂q̂(1/n₁ + 1/n₂)) STAT ▸ TESTS ▸ 6:2-PropZTest
p̂ = (x₁ + x₂)/(n₁ + n₂) (pooled) STAT ▸ TESTS ▸ B:2-PropZInt
CI uses √(p̂₁q̂₁/n₁ + p̂₂q̂₂/n₂) Enter x₁, n₁, x₂, n₂


Counts & categories
6. Chi-square tests (Ch. 15)
Statistic: χ² = Σ (O − E)² / E. Condition: every expected count ≥ 5.
Test df TI-84
Goodness-of-fit k−1 D:χ²GOF-Test — Obs in L1, Exp in L2
Independence / Homogeneity (r−1)(c−1) Table → matrix [A], C:χ²-Test;
expected go to [B]
p-value from a χ² — χ²cdf(χ², 1E99, df)
Standardized residual (which cell drives a significant result) = (O − E)/√E — compute by hand
from [A] and [B]; |value| > 2 is notable.

Association
7. Linear regression (Ch. 16–17)
Use when: two quantitative variables. Conditions = LINE. df = n − 2.
Formula TI-84 (F:LinRegTTest)
b₁ = r · (s_y / s_x); b₀ = ȳ − b₁x̄ Output: a = b₀, b = b₁, r², r
t = b₁ / SE(b₁), test H₀: β₁ = 0 Output: t, p, df, s = s_e
SE(b₁) = s_e / (s_x·√(n−1)) Not shown directly → SE(b₁) = b / t
CI: b₁ ± t*₍ₙ₋₂₎ · SE(b₁) By hand with invT(area_left, n−2)
ŷ = b₀ + b₁x ; R² = r² Residuals stored in the RESID list
Alternative: in LinRegTTest set β & ρ to ≠0, <0, or >0 to match H_A; the ≠0 p-value halves for a
one-sided test. Prediction / mean-response intervals have no built-in command — compute by
hand.