CAIE S2 2020 June — Question 2

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2020
SessionJune
TopicHypothesis test of binomial distributions
TypeState hypotheses with additional parts

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.
  1. State suitable null and alternative hypotheses for the test.
  2. Find the probability of a Type I error.
    In fact 2 of the 25 apples were Grade A .
  3. Which of the errors, Type I or Type II, is possible? Justify your answer.