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  • Perplex
    IB Math AIHL
    /
    Inference & Hypotheses
    /

    Problem Bank

    [Maximum mark: 7]

    The number of defective widgets produced by a machine in a batch of ​40​ can be modeled by a binomial distribution. The manufacturer claims the defect rate is ​5%. An inspector, Lee, believes the true defect rate is higher and decides to conduct a test:

    • He inspects one batch of 40 widgets.

    • If he finds 3 or more defectives, he will reject the manufacturer’s claim.

    1. State a suitable null and alternative hypothesis for Lee’s test.

      [2]
    2. Find the probability of a Type  I error.

      [2]

    Suppose the true defect rate is actually ​8%.

    1. Find the probability of a Type  II error.

      [3]

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