Type I and Type II errors

Type I and Type II errors Quiz

Spec SC1 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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1. Which statement defines a Type II error?
- A. Rejecting $\mathrm{H}_0$ when it is true
- B. Not rejecting $\mathrm{H}_0$ when it is false
- C. Rejecting $\mathrm{H}_0$ when it is false
- D. Not rejecting $\mathrm{H}_0$ when it is true
2. $X\sim\mathrm{B}(10,p)$ . $\mathrm{H}_0:p=0.5$ , $\mathrm{H}_1:p>0.5$ , reject $\mathrm{H}_0$ if $X\ge9$ . Find $\mathrm{P}$ (Type I error).
- A. $0.0547$
- B. $0.0098$
- C. $0.0107$
- D. $0.9893$
3. The critical region of a test is made larger. What happens to the probability of a Type I error?
- A. It increases
- B. It decreases
- C. It stays the same
- D. It becomes zero
4. $X\sim\mathrm{Po}(2)$ under $\mathrm{H}_0$ . Reject $\mathrm{H}_0$ if $X\ge6$ . Find $\mathrm{P}$ (Type I error).
- A. $0.0120$
- B. $0.9834$
- C. $0.0361$
- D. $0.0166$
5. A test checks whether a new drug raises the recovery rate above 60%. What is a Type I error in context?
- A. Concluding the rate is above 60% when it is really 60%
- B. Concluding the rate is 60% when it is really above 60%
- C. Concluding the rate is above 60% when it is really above 60%
- D. Concluding the rate is below 60% when it is really 60%