Estimate the true population mean with a stated level of confidence - a core AI HL inference skill.
In short: A confidence interval for a mean gives a range of plausible values for the population mean, based on a sample. The GDC's t-interval takes the sample data or summary values and a confidence level, then returns the lower and upper limits. Interpret it as a range of plausible values for the mean, not as a probability.
When you'd use this
Estimating a population mean from a sample, with a stated level of confidence (e.g. 95%).
The population standard deviation is unknown, so the interval uses the t-distribution, not z.
A question asks for both the interval and an interpretation of what it means.
Checking whether a claimed population mean falls inside or outside your interval.
At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared
TI-84 Plus CE
Casio fx-CG50 and fx-CG100
TI-Nspire CX
Key sequence
STAT → TESTS → TInterval; choose Stats and enter x̄, s and n; set the confidence level C and calculate.
Main menu → Statistics → INTR → t → 1-SAMPLE; enter x̄, s, n and the confidence level.
menu → Statistics → Stat Tests → t Interval; enter x̄, s, n and the confidence level.
On a TI-84 Plus CE
Identify the sample mean x̄, sample standard deviation s, sample size n, and the confidence level (e.g. 95%).
STAT → TESTS → TInterval; choose Stats and enter x̄, s and n; set the confidence level C and calculate.
The calculator outputs the interval (a, b). Write it as a ≤ μ ≤ b.
The margin of error E = (b − a) / 2; the sample mean x̄ = (a + b) / 2.
Tip: A 95% CI means: if you repeated the sampling many times, 95% of the intervals would contain the true mean - not that there is a 95% chance μ is in this specific interval.
Tip: A wider interval means less precision. To halve the margin of error you must quadruple the sample size.
On a Casio fx-CG50 and fx-CG100
Identify the sample mean x̄, sample standard deviation s, sample size n, and the confidence level (e.g. 95%).
Main menu → Statistics → INTR → t → 1-SAMPLE; enter x̄, s, n and the confidence level.
The calculator outputs the interval (a, b). Write it as a ≤ μ ≤ b.
The margin of error E = (b − a) / 2; the sample mean x̄ = (a + b) / 2.
Tip: A 95% CI means: if you repeated the sampling many times, 95% of the intervals would contain the true mean - not that there is a 95% chance μ is in this specific interval.
Tip: A wider interval means less precision. To halve the margin of error you must quadruple the sample size.
On a TI-Nspire CX
Identify the sample mean x̄, sample standard deviation s, sample size n, and the confidence level (e.g. 95%).
menu → Statistics → Stat Tests → t Interval; enter x̄, s, n and the confidence level.
The calculator outputs the interval (a, b). Write it as a ≤ μ ≤ b.
The margin of error E = (b − a) / 2; the sample mean x̄ = (a + b) / 2.
Tip: A 95% CI means: if you repeated the sampling many times, 95% of the intervals would contain the true mean - not that there is a 95% chance μ is in this specific interval.
Tip: A wider interval means less precision. To halve the margin of error you must quadruple the sample size.
Here's a real IB-style question that uses exactly this technique.
HardCalculatorPaper 2[4 marks]
A sample of 10 values has mean 24 and standard deviation 3. Find a 95% confidence interval for the population mean.
(21.9, 26.1)
Mark it
Correct4 / 4 marks
Worked solution & mark scheme:
M1 Use a 1-sample t-interval with x̄ = 24, s = 3, n = 10
A1 (21.9, 26.1)
Common questions
When would I need to find a confidence interval for a mean in IB Maths?
Estimate the true population mean with a stated level of confidence - a core AI HL inference skill. Estimating a population mean from a sample, with a stated level of confidence (e.g. 95%). The population standard deviation is unknown, so the interval uses the t-distribution, not z.
How do I find a confidence interval for a mean on a TI-84 Plus CE?
1. Identify the sample mean x̄, sample standard deviation s, sample size n, and the confidence level (e.g. 95%). 2. STAT → TESTS → TInterval; choose Stats and enter x̄, s and n; set the confidence level C and calculate. 3. The calculator outputs the interval (a, b). Write it as a ≤ μ ≤ b. 4. The margin of error E = (b − a) / 2; the sample mean x̄ = (a + b) / 2.
How do I find a confidence interval for a mean on a Casio fx-CG50 and fx-CG100?
1. Identify the sample mean x̄, sample standard deviation s, sample size n, and the confidence level (e.g. 95%). 2. Main menu → Statistics → INTR → t → 1-SAMPLE; enter x̄, s, n and the confidence level. 3. The calculator outputs the interval (a, b). Write it as a ≤ μ ≤ b. 4. The margin of error E = (b − a) / 2; the sample mean x̄ = (a + b) / 2.
How do I find a confidence interval for a mean on a TI-Nspire CX?
1. Identify the sample mean x̄, sample standard deviation s, sample size n, and the confidence level (e.g. 95%). 2. menu → Statistics → Stat Tests → t Interval; enter x̄, s, n and the confidence level. 3. The calculator outputs the interval (a, b). Write it as a ≤ μ ≤ b. 4. The margin of error E = (b − a) / 2; the sample mean x̄ = (a + b) / 2.
What should I watch out for when I find a confidence interval for a mean?
A 95% CI means: if you repeated the sampling many times, 95% of the intervals would contain the true mean - not that there is a 95% chance μ is in this specific interval. A wider interval means less precision. To halve the margin of error you must quadruple the sample size.
How are marks awarded when I find a confidence interval for a mean in an IB exam?
In the worked example on this page (4 marks, Paper 2), the marks are: M1: Use a 1-sample t-interval with x̄ = 24, s = 3, n = 10; A1: (21.9, 26.1).
