Type II errors and power

Type II errors and power Quiz

Spec SC2 · AQA A-Level Further Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

  1. 1. Which statement describes the power of a test?

    • A. The probability of a Type I error
    • B. The probability of rejecting H0\mathrm{H}_0 when H1\mathrm{H}_1 is true
    • C. The probability of not rejecting H0\mathrm{H}_0 when it is false
    • D. The significance level

  2. 2. Reject H0\mathrm{H}_0 if xˉ>10.5\bar x>10.5. The true distribution is xˉ∼N(11,1)\bar x\sim\mathrm{N}(11,1). Find P\mathrm{P}(Type II error).

    • A. 0.69150.6915
    • B. 0.19150.1915
    • C. 0.06680.0668
    • D. 0.30850.3085

  3. 3. Reject H0\mathrm{H}_0 if X≥7X\ge7 where X∼Po(λ)X\sim\mathrm{Po}(\lambda). The true value is λ=4\lambda=4. Find P\mathrm{P}(Type II error).

    • A. 0.88930.8893
    • B. 0.11070.1107
    • C. 0.78510.7851
    • D. 0.94890.9489

  4. 4. The true value of the parameter moves further from the H0\mathrm{H}_0 value. What happens to the power?

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

  5. 5. The critical region is enlarged. Which statement is correct?

    • A. Both error probabilities increase
    • B. P\mathrm{P}(Type I) increases and P\mathrm{P}(Type II) decreases
    • C. Both error probabilities decrease
    • D. P\mathrm{P}(Type I) decreases and P\mathrm{P}(Type II) increases

Quiz