In a game, a ball is thrown and lands in one of 4 slots, labelled A, B, C and D. Raju wishes to test whether the probability that the ball will land in slot A is 1/4. The ball is thrown 100 times and it lands in slot A 15 times.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [1] (a) Ho: p = 1/4 or Ho: μ = 25; H1: p≠ 1/4 or H₁: μ ≠ 25
2. [B1] (b) N(25, 75/4) Allow B1 for N(25, 75/4) or N(0.25,0.001875) SOI.
3. [M1] (b) Standardise with their N(25,...); Allow with no or wrong continuity correction.
4. [A1] (b) ± -2.194 (2.19)
5. [M1] (b) -2.326 < -2.194 or 0.0141 > 0.01 or 0.9859 < 0.99
6. [A1 FT] (b) No evidence to reject that the probability is 1/4; OE must be in context and not definite, e.g. not 'Claim untrue'. No contradictions. FT their z; dependent on two-tailed test (one-tailed test can score B1 M1 A1 M1 A0) SC for use of Binomial B(100,0.25) P = 0.0111 for B1 and then comparison with 0.01 and correct conclusion for B1, maximum 2 out of 5 marks.