Type I and Type II errors and power

Type I and Type II errors and power Quiz

Spec 8.1 · Edexcel A-Level Further Maths: Quiz

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  1. 1. A new drug is tested and H0\mathrm{H}_0 states that it has no effect. In reality it has no effect, but the test rejects H0\mathrm{H}_0. This is:

    • A. A Type II error
    • B. Correct decision
    • C. A Type I error
    • D. A large power

  2. 2. The probability of a Type II error at a particular alternative value is 0.350.35. What is the power at that value?

    • A. 0.350.35
    • B. 0.650.65
    • C. 0.50.5
    • D. 1.351.35

  3. 3. X∼B(20,p)X\sim\mathrm{B}(20,p) is used to test H0:p=0.1\mathrm{H}_0:p=0.1 with critical region X≥5X\geq5. Which probability is the size of the test?

    • A. P(X≥5∣p=0.1)\mathrm{P}(X\geq5\mid p=0.1)
    • B. P(X≤4∣p=0.1)\mathrm{P}(X\leq4\mid p=0.1)
    • C. P(X≥5∣p=0.3)\mathrm{P}(X\geq5\mid p=0.3)
    • D. P(X≤4∣p=0.3)\mathrm{P}(X\leq4\mid p=0.3)

  4. 4. For the same test, which probability is the probability of a Type II error when p=0.3p=0.3?

    • A. P(X≥5∣p=0.3)\mathrm{P}(X\geq5\mid p=0.3)
    • B. P(X≤4∣p=0.1)\mathrm{P}(X\leq4\mid p=0.1)
    • C. P(X≥5∣p=0.1)\mathrm{P}(X\geq5\mid p=0.1)
    • D. P(X≤4∣p=0.3)\mathrm{P}(X\leq4\mid p=0.3)

  5. 5. A sample size is increased while the size of the test is kept the same. What happens to the power at a fixed alternative?

    • A. It increases
    • B. It decreases
    • C. It stays the same
    • D. It becomes the size

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