A-level · Hypothesis testing

One-tailed tests (the probability method)Exam-style questions

Carrying out a one-tailed binomial hypothesis test by the probability (p-value) method: assume H0, model X ~ B(n, p0), find the probability of a result at least as extreme as the one observed in the direction of H1 — P(X ≥ x) for an upper test or P(X ≤ x) for a lower test — compare it with the significance level, and write a full conclusion in context.

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11 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
A test of $H_0: p = 0.3$ against $H_1: p > 0.3$ uses $X \sim B(20, 0.3)$ and observes $X = 10$ . Using a $5\%$ significance level, carry out the test.
Level 3 · 4 marksTry it
2
At a market stall, customers are offered a taste of a cheese before they decide whether to buy any.

Over a long period, Lena has found that $40\%$ $40%$ of the customers who taste this cheese then buy some.

Lena changes the way the cheese is displayed on her stall and claims that the proportion of customers who taste the cheese and then buy some has increased.

A random sample of $30$ $30$ customers who taste the cheese after the change is taken and $18$ $18$ of them buy some cheese.

Use a suitable test to assess Lena's claim.

You should
- state your hypotheses clearly
- use a $5\%$ level of significance
(4 marks)
Level 3 · 4 marksTry it