IB Maths AI SL · Unit 4: Statistics and Probability
IB Maths AI SL Two-Sample T-Test Questions
Exam-style IB Maths AI SL two-sample t-test questions with worked solutions. Start with the 3 fully worked examples below — each is solved step by step the way an IB examiner expects — then try the practice questions and check your working against the mark scheme.
- 10 questions
- Paper 1: 4
- Paper 2: 6
- 2 easy
- 4 medium
- 2 hard
- 2 very hard
- 3 worked examples
Practise Two-Sample T-Test questions →
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What's examined in AI SL two-sample t-test
The question bank covers these two-sample t-test question types (number of questions in brackets):
- Performing the Test (5)
- Hypotheses and Assumptions (4)
- Interpreting Test Results (1)
Two-Sample T-Test worked examples
Worked example 1: Stating t-test hypotheses · easy
A biologist claims chinchilla rabbits have a greater mean weight than sable rabbits. Write $H_0$ and $H_1$ using $\mu_c$ and $\mu_s$.
1. Recall: $H_0$ always assumes equality.
2. $H_0$: $\mathbf{\mu_c = \mu_s}$ — the population mean weight of chinchilla equals that of sable rabbits.
3. Extract claim: "strictly greater".
4. $H_1$: $\mathbf{\mu_c > \mu_s}$ — the population mean weight of chinchilla rabbits is greater than that of sable rabbits.
Examiner tip: Always use the phrase "population mean" when defining $t$-test hypotheses in words — "sample mean" loses marks.
Worked example 2: Conducting an unpooled two-sample t-test · medium
Diet A: $1.2, 1.4, 1.3, 1.5, 1.4$ kg. Diet B: $1.5, 1.6, 1.4, 1.7, 1.6$ kg. Do a two-tailed, unpooled $t$-test on the GDC and state the $p$-value.
1. Enter: Diet A in List 1, Diet B in List 2.
2. Navigate: 2-Sample $t$-test.
3. Set: alternative $\mu_1 \ne \mu_2$ (two-tailed).
4. Pooled: OFF (Unpooled), as required by the AI syllabus.
5. Execute: $p = 0.016335\ldots \Rightarrow \mathbf{0.0163}$.
Examiner tip: Confirm your GDC is set to Unpooled — pooling assumes equal population variances, which is outside AI SL.
Worked example 3: Interpreting the t-test conclusion at 1% · hard
Given $p = 0.0163$ from the previous test, write your conclusion at the $1\%$ significance level.
1. $p$-value: $0.0163$.
2. Threshold: $1\% = 0.01$.
3. Compare: $0.0163 > 0.01$.
4. Decision: fail to reject $H_0$.
5. Conclude: insufficient evidence at the $1\%$ level to conclude a difference between the mean weights of fish on Diet A and Diet B.
Examiner tip: Pay attention to the requested significance level — $p=0.0163$ rejects at $5\%$ but not at the stricter $1\%$.
Try these IB Maths AI SL two-sample t-test questions
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
Question 1 · easy · 3 marks · Paper 1
A researcher conducts a two-sample \(t\)-test to determine if there is a difference in the mean lifetimes of two brands of lightbulbs, Brand A and Brand B.
- State the null hypothesis, \(H_0\), for this test.
- State the alternative hypothesis, \(H_1\), for this test.
- Identify whether this is a one-tailed or two-tailed test.
Question 2 · medium · 3 marks · Paper 2
A two-sample \(t\)-test is performed at a \(5\%\) significance level to compare the mean reading speeds of two different age groups. Technology output gives a \(p\)-value of \(0.027\).
- State the condition for rejecting the null hypothesis in terms of the \(p\)-value.
- Write down the conclusion of the test, giving a clear reason.
Question 3 · hard · 5 marks · Paper 2
A botanist is testing whether a new fertilizer (Fertilizer B) produces taller plants on average than the current fertilizer (Fertilizer A). She records the heights in cm:
Fertilizer A: \(12, 15, 14, 11, 16, 14, 13\)
Fertilizer B: \(16, 18, 17, 14, 19, 17, 16, 18\)
Assuming the heights are normally distributed with equal variances, she performs an unpaired two-sample \(t\)-test at the \(1\%\) level of significance.
- State the alternative hypothesis for this test.
- Using your GDC, find the \(p\)-value for this test.
- State your conclusion in context.
All 10 two-sample t-test questions with mark schemes →
FAQ
How many IB Maths AI SL two-sample t-test questions are there?
There are 10 exam-style two-sample t-test questions in the AI SL question bank (Paper 1: 4 · Paper 2: 6), graded 2 easy, 4 medium, 2 hard, 2 very hard. Every question has a full IB-style mark scheme (M, A and R marks).
Is two-sample t-test on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 4 · Paper 2: 6. Practise with your GDC — AI papers expect calculator methods throughout.
Where can I get the mark schemes?
Open the AI SL Unit 4 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.
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