Test whether two independent groups have different population means - e.g. comparing test scores from two classes.
In short: A two-sample t-test compares the means of two independent groups to see whether the difference between them is statistically significant. Enter both data sets or their summary statistics, choose the tail and whether to pool the variances, then read the t statistic and p-value. Compare the p-value with the significance level.
When you'd use this
Comparing the means of two independent groups, e.g. two classes' test scores.
Both samples are roughly normal and you have each sample's mean, standard deviation and size.
Deciding whether an observed difference between two groups is statistically significant.
The population standard deviations are unknown, so a z-test isn't appropriate.
Here's a real IB-style question that uses exactly this technique.
HardCalculatorPaper 2[4 marks]
Sample 1: mean 48, sd 5, n = 12. Sample 2: mean 52, sd 6, n = 14. Test H₀: μ₁ = μ₂ against H₁: μ₁ ≠ μ₂ at the 5% significance level.
t = -1.83, p = 0.0801 > 0.05, so fail to reject H₀
Mark it
Correct4 / 4 marks
Worked solution & mark scheme:
M1 Enter both samples' summary statistics into a 2-sample t-test
A1 t = -1.83, p = 0.0801
R1 p > 0.05: insufficient evidence of a difference in means
Common questions
When would I need to do a two-sample t-test in IB Maths?
Test whether two independent groups have different population means - e.g. comparing test scores from two classes. Comparing the means of two independent groups, e.g. two classes' test scores. Both samples are roughly normal and you have each sample's mean, standard deviation and size.
How do I do a two-sample t-test on a TI-84 Plus CE?
1. State H₀: μ₁ = μ₂ and H₁: μ₁ ≠ μ₂ (or one-tailed), plus the significance level. 2. Check that both populations are approximately normal and the samples are independent. 3. STAT → TESTS → 2-SampTTest; choose Data (lists) or Stats (enter x̄, s, n for each group); select the tail and calculate. 4. Read the p-value and t-statistic; compare p to the significance level to write your conclusion.
How do I do a two-sample t-test on a Casio fx-CG50 and fx-CG100?
1. State H₀: μ₁ = μ₂ and H₁: μ₁ ≠ μ₂ (or one-tailed), plus the significance level. 2. Check that both populations are approximately normal and the samples are independent. 3. Main menu → Statistics → TEST → t → 2-SAMPLE; enter x̄, s and n for each group, set the tail. 4. Read the p-value and t-statistic; compare p to the significance level to write your conclusion.
How do I do a two-sample t-test on a TI-Nspire CX?
1. State H₀: μ₁ = μ₂ and H₁: μ₁ ≠ μ₂ (or one-tailed), plus the significance level. 2. Check that both populations are approximately normal and the samples are independent. 3. menu → Statistics → Stat Tests → 2-Sample t Test; enter the summary statistics or select the data columns. 4. Read the p-value and t-statistic; compare p to the significance level to write your conclusion.
What should I watch out for when I do a two-sample t-test?
Use pooled variance only if the question explicitly states the variances are equal - otherwise leave it unpooled (the default).
How are marks awarded when I do a two-sample t-test in an IB exam?
In the worked example on this page (4 marks, Paper 2), the marks are: M1: Enter both samples' summary statistics into a 2-sample t-test; A1: t = -1.83, p = 0.0801; R1: p > 0.05: insufficient evidence of a difference in means.
