May/June 2026 Paper 61

2026 · 6 questions · 17 parts · 50 marks

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Context for question 2
In the past, 2% of talking dolls made by a certain firm have been faulty. Following a change in the manufacturing process, a quality control officer suspects that the percentage of faulty talking dolls has increased. In order to test his suspicion, he selects 50 talking dolls at random. If the number of faulty talking dolls is more than 3, he will conclude that the percentage has increased.
2(a)Hypothesis TestingMedium1 mark
State suitable null and alternative hypotheses for the test.
2(b)Hypothesis TestingMedium1 mark
State what is meant by a Type II error in this context.
2(c)Hypothesis TestingMedium3 marks
Given that the true percentage of faulty talking dolls is now , use a binomial distribution to find the probability of a Type II error.
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Probability