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t-tests: IB Mathematics: Applications & Interpretation questions with answers Free t-tests questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.
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t-tests practice questions Question 1 Structured · 5 marks
Two groups of students used different revision methods. A t-test is used to compare their mean scores at the 5% significance level.
(a) State suitable null and alternative hypotheses.
[2] (b) The p-value is 0.041. State the conclusion of the test, with a reason.
[2] (c) State one assumption needed for the t-test.
[1] Show answers and mark scheme Part Answer and marking points Marks (a) H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂H₀: μ₁ = μ₂ A1 A1
2 (b) reject H₀0.041 < 0.05 R1 A1
2 (c) normal distributions / equal variancesdata normally distributed (or equal population variances) R1
1
Question 2 Structured · 6 marks
A teacher tests whether a new revision method improves scores. The scores of two groups are shown.
Old method 57 66 59 63 69 57 60 63 New method 74 79 70 67 68 76 79
Table 2.1
(a) State suitable hypotheses for a one-tailed test.
[2] (b) Use a pooled two-sample t-test to find the p-value.
[2] (c) State the conclusion at the 5% significance level.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) H0 : μnew = μold ; H1 : μnew > μold H0 : μnew = μold A1 1 : μnew > μold A1
2 (b) 1.75 × 10−4 GDC two-sample t-test, pooled (M1) −4 A1
2 (c) reject H0 1.75 × 10−4 < 0.05 R1 0 : there is evidence the new method improves scores A1
2
Question 3 Structured · 5 marks
Two groups of students used different revision methods. A t-test is used to compare their mean scores at the 5% significance level.
(a) State suitable null and alternative hypotheses.
[2] (b) The p-value is 0.12. State the conclusion of the test, with a reason.
[2] (c) State one assumption needed for the t-test.
[1] Show answers and mark scheme Part Answer and marking points Marks (a) H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂H₀: μ₁ = μ₂ A1 A1
2 (b) do not reject H₀0.12 > 0.05 R1 A1
2 (c) normal distributions / equal variancesdata normally distributed (or equal population variances) R1
1
Question 4 Structured · 5 marks
Two groups of students used different revision methods. A t-test is used to compare their mean scores at the 5% significance level.
(a) State suitable null and alternative hypotheses.
[2] (b) The p-value is 0.087. State the conclusion of the test, with a reason.
[2] (c) State one assumption needed for the t-test.
[1] Show answers and mark scheme Part Answer and marking points Marks (a) H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂H₀: μ₁ = μ₂ A1 A1
2 (b) do not reject H₀0.087 > 0.05 R1 A1
2 (c) normal distributions / equal variancesdata normally distributed (or equal population variances) R1
1
Question 5 Structured · 5 marks
Two groups of students used different revision methods. A t-test is used to compare their mean scores at the 5% significance level.
(a) State suitable null and alternative hypotheses.
[2] (b) The p-value is 0.023. State the conclusion of the test, with a reason.
[2] (c) State one assumption needed for the t-test.
[1] Show answers and mark scheme Part Answer and marking points Marks (a) H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂H₀: μ₁ = μ₂ A1 A1
2 (b) reject H₀0.023 < 0.05 R1 A1
2 (c) normal distributions / equal variancesdata normally distributed (or equal population variances) R1
1
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Meet Riyaz → Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in