Confidence Intervals on TI-84 — ZInterval, TInterval & More

Calculate a confidence interval on the TI-84 in three steps — then write the AP Statistics interpretation sentence correctly.

Which Interval Do You Need?

Quick rule: If the problem gives you σ (population standard deviation), use ZInterval. In almost every AP Statistics problem, σ is unknown — use TInterval.

Running a TInterval (One Sample Mean)

Example: You measure 25 students' study hours. x̄ = 6.4 hours, s = 1.8 hours. Calculate a 95% confidence interval.

Steps:

1. Press STAT
2. Arrow right to TESTS
3. Select 8: TInterval
4. Choose Stats
5. Enter:
   • x̄ = 6.4
   • Sx = 1.8
   • n = 25
   • C-Level = 0.95
6. Highlight Calculate → press ENTER

Output:

(5.6567, 7.1433)
x̄ = 6.4
Sx = 1.8
n = 25

The interval (5.6567, 7.1433) is your answer.

Reading the Output

The calculator does not show the margin of error directly. If you need it: margin of error = (upper − lower) ÷ 2 = (7.143 − 5.657) ÷ 2 = 0.743.

Writing the AP Statistics Interpretation

This is the sentence that gets full credit. The format has three required parts:

Template:

"We are [C-Level]% confident that the true [parameter in context] is between [lower] and [upper] [units]."

For our example:

"We are 95% confident that the true mean number of study hours per day for all students is between 5.66 and 7.14 hours."

⚠️ Common AP grading error: Do not write "there is a 95% probability the true mean is in this interval." The true mean is fixed — the interval is random. Write "we are 95% confident."

Running a 1-PropZInt (Proportion)

Example: 156 out of 400 voters support a policy. Calculate a 90% confidence interval for the true proportion.

1. Press STAT → TESTS → A: 1-PropZInt
2. Enter:
   • x = 156 (count of successes — enter the raw number, not the proportion)
   • n = 400
   • C-Level = 0.90
3. Select Calculate → ENTER

Output:

(0.3502, 0.4298)
p̂ = 0.39
n = 400

Interpretation:

"We are 90% confident that the true proportion of voters who support this policy is between 35.0% and 43.0%."

What Changes the Width of an Interval?

Understanding this helps you answer AP free-response questions about interval width:

The only thing you control that narrows an interval is increasing n.

Common Mistakes

1. Entering the proportion instead of the count For 1-PropZInt, the calculator asks for x = the number of successes (e.g. 156), not p̂ (0.39). Enter the raw count.

2. Using ZInterval when σ is unknown If the problem gives you s (sample standard deviation), use TInterval. ZInterval requires the true population σ, which is rarely known.

3. Misinterpreting the interval The interval estimates the population parameter, not future individual values. "We are 95% confident the next student will study 5.66 to 7.14 hours" is wrong.

4. Forgetting units in the interpretation sentence Always include units (hours, dollars, proportion, etc.) in your conclusion.

Checking Conditions

AP Statistics requires condition verification before calculating:

For TInterval:

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

For 1-PropZInt:

• Random sample ✓
• n·p̂ ≥ 10 and n·(1−p̂) ≥ 10 ✓
• Independent (n ≤ 10% of population) ✓

Practice calculating confidence intervals on the free TI-84 calculator.

Open TI-84 Calculator →

Related Guides

• Hypothesis Testing on TI-84 — Z-Test, T-Test & Proportion Test
• Linear Regression on TI-84 — LinReg Step by Step
• IB Math TI-84 Reference Guide