Hypothesis Testing on TI-84 — Z-Test, T-Test & Proportion Test

Run a hypothesis test on the TI-84 Plus CE in under two minutes — then use the output to write a complete AP Statistics conclusion.

Which Test Do You Need?

Before touching the calculator, match your situation to the right test:

Not sure? If you're working with counts or percentages (e.g. "42 out of 100 students"), use 1-PropZTest. If you're working with measurements and averages, use T-Test (σ is almost never known in AP Stats).

Running a T-Test (One Sample)

This is the most common test in AP Statistics.

Example: A teacher claims the average exam score is 75. You sample 30 students and find x̄ = 78.4, s = 9.2. Test at α = 0.05.

Steps:

1. Press STAT
2. Arrow right to TESTS
3. Select 2: T-Test
4. Choose Stats (if you already have x̄, s, and n) or Data (if your numbers are in a list)
5. Enter your values:
   • μ₀ = 75 (the null hypothesis value)
   • x̄ = 78.4
   • Sx = 9.2
   • n = 30
6. Set the alternative hypothesis μ:
   • ≠ μ₀ for two-tailed (most common)
   • < μ₀ or > μ₀ for one-tailed
7. Highlight Calculate and press ENTER

Reading the T-Test Output

The screen shows several values. Here is what each one means:

The only number that decides your conclusion is p.

Writing the AP Statistics Conclusion

This is what most guides skip. Here are the exact sentence templates:

If p < α (reject H₀):

"Since p = [value] < α = [0.05], we reject H₀. We have sufficient evidence that [restate alternative hypothesis in context]."

If p ≥ α (fail to reject H₀):

"Since p = [value] ≥ α = [0.05], we fail to reject H₀. We do not have sufficient evidence that [restate alternative hypothesis in context]."

For our example (p = 0.0523 ≥ 0.05):

"Since p = 0.0523 ≥ α = 0.05, we fail to reject H₀. We do not have sufficient evidence that the true mean exam score differs from 75."

⚠️ Never write "accept H₀" — AP graders will mark this wrong. Always write "fail to reject."

Running a 1-PropZTest (Proportion)

Example: You claim more than 60% of students pass. In a sample of 80 students, 54 pass. Test at α = 0.05.

1. Press STAT → TESTS → 5: 1-PropZTest
2. Enter:
   • p₀ = 0.60 (null hypothesis proportion)
   • x = 54 (number of successes)
   • n = 80 (sample size)
3. Set alternative: prop > p₀ (one-tailed, right)
4. Select Calculate → ENTER

Output:

• z = 0.913 — test statistic
• p = 0.1806 — p-value
• p̂ = 0.675 — your sample proportion

Conclusion: Since p = 0.1806 ≥ α = 0.05, we fail to reject H₀. We do not have sufficient evidence that more than 60% of students pass.

Common Mistakes

1. Choosing the wrong tail direction ≠ is two-tailed (splits α in half). If the problem says "more than" or "less than," use a one-tailed test (> or <). If it just says "differs" or "changed," use two-tailed.

2. Confusing x and p̂ The calculator asks for x (the raw count, e.g. 54), not the proportion (0.675). Enter the count.

3. Reading t instead of p The test statistic t tells you direction and magnitude. The p-value is what you compare to α. Don't compare t to α.

4. Writing "accept H₀" In AP Statistics, you never accept the null. You either reject it or fail to reject it.

Checking Conditions Before You Run the Test

AP Statistics requires you to verify conditions before calculating. The TI-84 won't do this for you.

For T-Test:

• Random sample ✓
• n ≥ 30, or population is approximately normal ✓
• Independent observations ✓

For 1-PropZTest:

• Random sample ✓
• np₀ ≥ 10 and n(1−p₀) ≥ 10 ✓ (check this by hand before running the test)
• Independent (n ≤ 10% of population) ✓

Practice running these tests on the free TI-84 calculator — no download required.

Open TI-84 Calculator →

Related Guides

• Confidence Intervals on TI-84 — ZInterval, TInterval & More
• Linear Regression on TI-84 — LinReg Step by Step
• IB Math TI-84 Reference Guide