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S2 exam technique

Edexcel IAL Mathematics · WST02 Statistics 2

The S2 paper (WST02) is a 1 hour 30 minute written exam worth 75 marks. Answer all questions; a calculator is allowed and the Mathematical Formulae and Statistical Tables booklet is provided. These habits come straight from Pearson's examiners' reports and mark schemes.

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Hypothesis tests

Hypotheses in terms of p or λ, with H0 and H1 labelled. Missing hypotheses can cost the final conclusion mark too.
Show the probability statements that justify a critical region; give the region as an inequality or set, not a probability.
Two-tailed: check both tails and use α/2 in each.
Two-part conclusion: 'reject H0' (or 'in the critical region', 'significant') and a sentence in context with the key words of the question, about a rate for Poisson. Do not contradict yourself.

Distributions and conditions

Poisson conditions must be in context: 'calls arrive singly, independently, at a constant rate'. Say constant rate, not constant probability.
To justify a Poisson approximation to the binomial, give both n large and p small.
If asked for an approximation, use it: an exact answer usually scores little or nothing.
Write the approximating distribution with parameters, such as N(60, 42), and always use a continuity correction.

Continuous random variables

Give the cdf for all x, including the 0 and 1 lines.
Solve F(m) = 0.5 for the median; do not work out F(0.5). Reject roots outside the range.
Use symmetry where you can (mean, median, constants).
Write substituted expressions, such as Var(X) = 12/5 - (3/2)², before the answer: relying on the calculator for too many steps loses marks.

Accuracy

Give answers to the accuracy asked; otherwise 3 significant figures, or exact fractions where they arise naturally. Probabilities from the tables are 4 d.p. and are accepted, as are calculator values.

Worked example

A student writes 'H0: the rate is 5, H1: the rate has increased', finds P(X ≥ 10) = 0.0318 under Po(5) and concludes 'reject H0'. How should the answer be improved?

Hypotheses must use the parameter: H0: λ = 5, H1: λ > 5.
Compare 0.0318 with 0.05 explicitly: 0.0318 < 0.05, so reject H0.
Add a contextual conclusion about the rate.

Answer: Write H0: λ = 5, H1: λ > 5, and add: 'There is evidence that the rate of [events] has increased.'

Key idea: Parameters in hypotheses; probabilities behind every critical region; two-part conclusions about a rate; conditions in context; full cdf; continuity corrections.

Check yourself

Which pair of hypotheses earns the mark?
- H0: the rate is 5, H1: the rate is more than 5
- H0: X = 5, H1: X > 5
- H0: λ = 5, H1: λ > 5
- H0: λ > 5, H1: λ = 5
Show answer
H0: λ = 5, H1: λ > 5. Hypotheses must be in terms of the parameter λ.
Which Poisson condition is written as the mark scheme requires?
- Customers enter the shop independently of each other
- Events are independent
- Each customer has a constant probability of entering
- The number of customers is fixed
Show answer
Customers enter the shop independently of each other. The condition is in context and correct.
A question says 'use a suitable approximation' for B(200, 0.02). A student uses the exact binomial. What is likely?
- Full marks, because the answer is more accurate
- A bonus mark for accuracy
- Few or no marks are scored
- Full marks if the answer is to 4 d.p.
Show answer
Few or no marks are scored. Mark schemes give little or no credit when the instructed method is not used.
Given F(x) for 0 ≤ x ≤ 2, how do you find the median?
- Calculate F(0.5)
- Solve F(m) = 0.5
- Solve f(m) = 0.5
- Find where f'(m) = 0
Show answer
Solve F(m) = 0.5. The median has half the probability below it.
The S2 paper has 75 marks in 90 minutes. About how many minutes should a 12-mark question take?
Show answer
14.4. 1.2 minutes per mark × 12 = 14.4, so about 14 minutes.
A two-tailed test is at the 6% level. A student uses 0.03 in each tail. Is this right?
- No, each tail should have 0.06
- Yes, because 6% split equally gives 0.03 in each tail
- No, each tail should have 0.015
- No, only one tail is used
Show answer
Yes, because 6% split equally gives 0.03 in each tail. α/2 = 6% ÷ 2 = 0.03 in each tail. A common error is to put the whole 0.06 in each tail instead of halving.

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Last updated 8 November 2026. Spotted a mistake? Tell us.