A-level · Hypothesis testing

Two-tailed testsExam-style questions

Carrying out a two-tailed binomial test (H1 : p ≠ p0), where a change in either direction counts as evidence. Splitting the significance level α into two tails of α/2, finding both critical regions and the actual significance level (the sum of the two tail probabilities), the equivalent p-value method (compare the observed tail with α/2, or 2× the tail with α), and writing a full conclusion in context.

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

DifficultyAllLevel 3Level 4
  1. 1
    A coin is tossed 2020 times and shows 1515 heads. Test, at the 5%5\% level, whether the coin is biased (H0:p=0.5H_0: p = 0.5, H1:p≠0.5H_1: p \ne 0.5).
    Level 3 · 4 marksTry it
  2. 2
    A claim states p=0.3p = 0.3. In a sample of 2525, X=3X = 3 is observed. Test H0:p=0.3H_0: p = 0.3 against H1:p≠0.3H_1: p \ne 0.3 at the 5%5\% level.
    Level 3 · 4 marksTry it
  3. 3
    A coin is tossed 4040 times and shows 2626 heads. Test, at the 5%5\% level, whether the coin is biased.
    Level 3 · 4 marksTry it
  4. 4
    A test of H0:p=0.4H_0: p = 0.4 against H1:p≠0.4H_1: p \ne 0.4 uses X∼B(30,0.4)X \sim B(30, 0.4) and observes X=6X = 6. Test at the 5%5\% level.
    Level 3 · 4 marksTry it
  5. 5
    Explain how a two-tailed test at the 5%5\% significance level is carried out differently from a one-tailed test at the same level.
    Level 3 · 2 marksTry it

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