IB Maths AI SL · Unit 4: Statistics and Probability
IB Maths AI SL Statistical Testing Questions
Exam-style IB Maths AI SL statistical testing 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.
- 24 questions
- Paper 1: 14
- Paper 2: 10
- 3 easy
- 5 medium
- 5 hard
- 4 very hard
- 7 starter
- 3 worked examples
Practise Statistical Testing questions →
AI SL formula booklet
What's examined in AI SL statistical testing
The question bank covers these statistical testing question types (number of questions in brackets):
- Chi-squared GoF Test (12)
- Chi-squared Independence Test (9)
- T-tests & Rank Correlation (3)
Statistical Testing worked examples
Worked example 1: Chi-squared expected frequency · easy
$150$ diners rate meals. $69$ are Children; $67$ ordered Shrimp. Under $H_0$, find the expected frequency of Children who ordered Shrimp.
1. Formula: $E = \frac{\text{Row} \times \text{Column}}{\text{Grand Total}}$.
2. Identify: Row $=69$, Column $=67$, Grand $=150$.
3. Substitute: $E = \frac{69 \times 67}{150}$.
4. Numerator: $69 \times 67 = 4623$.
5. Evaluate: $\frac{4623}{150} = \mathbf{30.8}$.
Examiner tip: Never round expected frequencies during working — keep exact decimals so the final $\chi^2$ statistic stays accurate.
Worked example 2: Chi-squared conclusion at 5% · medium
$\chi^2$ test at $5\%$ gives $\chi^2_{\text{calc}} = 8.54$, $p = 0.0736$. State $H_0$ and write the conclusion.
1. $H_0$: the two variables are independent (no association).
2. Extract: $p = 0.0736$.
3. Compare: $0.0736 > 0.05$.
4. Decision: do not reject $H_0$.
5. Context: insufficient evidence to suggest the variables are dependent.
Examiner tip: "Accept $H_1$" is poor mathematical phrasing. Always say "Reject $H_0$" or "Do not reject $H_0$".
Worked example 3: Chi-squared goodness of fit · hard
$147$ calls tracked over 7 days: $22,18,17,25,25,19,21$. Test if calls are uniform. State df and find $p$ using a GDC.
1. df: $k - 1 = 7 - 1 = \mathbf{6}$.
2. Expected: uniform $\Rightarrow \frac{147}{7} = 21$ per day.
3. Enter: observed $\{22,18,17,25,25,19,21\}$ and expected $\{21,\ldots,21\}$.
4. Execute: $\chi^2$ GOF with df $=6$.
5. Read: $p = 0.81467\ldots \Rightarrow \mathbf{0.815}$.
Examiner tip: GOF tests don't give you a contingency table — you must build the expected frequency list from the stated model (uniform, binomial, normal, etc.).
Try these IB Maths AI SL statistical testing 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
Abhinav carries out a \(\chi^2\) test for independence at the \(1\%\) significance level to determine whether a person’s gender is associated with their chosen professional field: Engineering, Medicine, or Law.
State the null hypothesis, \(H_0\), for this test.
State the alternative hypothesis, \(H_1\), for this test.
Question 2 · medium · 4 marks · Paper 2
A \(\chi^2\) test of independence is performed on a contingency table with 3 rows and 3 columns at the \(5\%\) significance level. The calculated \(\chi^2\) value is \(9.45\), and the software outputs a \(p\)-value of \(0.0508\).
- Calculate the number of degrees of freedom.
- State, with a reason, whether the null hypothesis should be rejected.
Question 3 · hard · 3 marks · Paper 1
A \(\chi^2\) test for independence is conducted on a contingency table that has 3 rows and 4 columns.
- Calculate the number of degrees of freedom for this test.
- If the significance level is \(5\%\) and the critical value is \(12.59\), state the condition under which the null hypothesis would be rejected using the test statistic \(\chi^2_{calc}\).
All 24 statistical testing questions with mark schemes →
FAQ
How many IB Maths AI SL statistical testing questions are there?
There are 24 exam-style statistical testing questions in the AI SL question bank (Paper 1: 14 · Paper 2: 10), graded 3 easy, 5 medium, 5 hard, 4 very hard, 7 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Is statistical testing on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 14 · Paper 2: 10. 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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