A-LevelMathematicsProbability and statistics9709/62 · May/June 2020 · Q26 Marks
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]
- (c)Which of the errors, Type I or Type II, is possible? Justify your answer.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] H0: Proportion = 0.05; H1: Proportion > 0.05
- [M1] 1-(0.95^25 + 25 × 0.95^24 × 0.05 + 25C2 × 0.95^23 × 0.05^2 + 25C3 × 0.95^22 × 0.05^3)
- [A1] Completely correct expression
- [A1] 0.0341
- [B1] Type II
- [B1] Will conclude proportion not increased
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