The two-sample t-test idea
Big idea: A two-sample t-test checks whether the MEANS of two groups are genuinely different, or whether the gap could just be chance.
Use it to compare two sets of measurements — for example the recovery times of runners on two training plans, or the heart rates of active vs non-active people.
t-test vs chi-squared: Use a t-test for the MEANS of numerical data.
Use chi-squared for COUNTS in categories.
Different data type → different test.
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it with your first topic free to keep:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
Hypotheses and tails
Choosing the tail: ‘lower than’ / ‘greater than’ → one-tailed (H1: mu1 < mu2 or mu1 > mu2). ‘different from’ → two-tailed (H1: mu1 != mu2).
Worked example
A coach claims runners on Plan A have a LOWER mean recovery time than Plan B.
State H0 and H1.
Step by step
- H0: the means are equal -> muA = muB
- ‘lower’ signals a one-tailed test
- H1: muA < muB
Final answer
H0: muA = muB; H1: muA < muB (one-tailed).
Stop wasting time on topics you know
Our AI identifies your weak areas and focuses your study time where it matters. No more overstudying easy topics.
Running the test on the GDC
Let the GDC do the arithmetic: Enter both data lists, run 2-SampTTest, and read the p-value.
Assume the data are normally distributed.
Set Pooled: Yes unless the question says the variances differ.
Worked example
Two lists are entered. 2-SampTTest with H1: mu1 < mu2 gives p = 0.018.
Test at the 5% significance level.
Solution
- Compare p with the significance level alpha = 0.05
- 0.018 < 0.05
Final answer
p < alpha, so reject H0.
Decision rule: p < significance level -> reject H0 (the means differ as claimed). p >= level -> fail to reject H0.
Interpretation and exam communication
Weak conclusion
- Only writes ‘reject H0’
- No context
- Never restates the claim
Strong conclusion
- States the decision in context
- Says which mean is larger/smaller
- Uses the significance level
Exam Tips:
- State H0 and H1 in words AND symbols.
- Match the tail to the wording (‘lower/greater’ = one-tailed, ‘different’ = two-tailed).
- Never write ‘accept H1’ — write ‘reject H0’ or ‘fail to reject H0’.
- The final sentence must answer the original claim in context.