Cambridge A Level Mathematics 9709 — 2020 May/June Paper 6 · Variant 2

2 A shop obtains apples from a certain farm. It has been found that 5% of apples from this farm are Grade A. Following a change in growing conditions at the farm, the shop management plan to carry out a hypothesis test to find out whether the proportion of Grade A apples has increased. They select 25 apples at random. If the number of Grade A apples is more than 3 they will conclude that the proportion has increased. (a) State suitable null and alternative hypotheses for the test. [1] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ (b) Find the probability of a Type I error. [3] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ In fact 2 of the 25 apples were Grade A. (c) Which of the errors, Type I or Type II, is possible? Justify your answer. [2] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mark scheme: 2(a) H1: Proportion > 0.05 1 2(b) 1 – (0.9525 + 25 × 0.9524 × 0.05 + 25C2 × 0.9523 × 0.052 + 25C3 × 0.9522 × 0.053) M1 Completely correct expression A1 0.0341 A1 3 2(c) Type II B1 Will conclude proportion not increased B1 2

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