Further Mathematics · Pearson Edexcel 9FM0 · Option FS1 · Topic 8

Quality of tests

How good a test is: Type I and Type II errors, the size of a test and its power.

  • 1 sub-topic
  • Taught in Year 13
  • 10 practice questions
  • 1 animated lesson
Practice questions (10) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 8.1Quality of testsY13

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Easy and hard questions from this topic, each with a worked solutions and the mark for every step. All 10 questions in this topic, free, no account needed.

Quality of tests

Not needed for Year 12Easy

Errors in hypothesis testing · Year 13 · 1 mark

  1. What is a Type II error?
    (1)

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  1. The power of a test is 1 − P(TypeIIerror)\mathrm{P}(Type II error).A: Not rejecting the null hypothesis when it is false

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Quality of tests

Not needed for Year 12Hard

The quality of a test · Year 13 · 6 marks

A test of H0:p=0.25H_0: p = 0.25 against H1:p>0.25H_1: p > 0.25 uses a sample of 30, at the 5% level of significance. XX is the number of successes.
  1. (a)
    Find the critical region for the test.
    (2)
  2. (b)
    Write down the size of the test.
    (1)
  3. (c)
    Find the power of the test when p=0.5p = 0.5, and explain what it means.
    (3)

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Part (a)2 marks

  1. The largest region with probability at most 0.05.P(X≥13)\mathrm{P}(X \geq 13)=0.0216≤0.05, P(X≥12){}= 0.0216 \leq 0.05, \ \mathrm{P}(X \geq 12)=0.0507>0.05{}= 0.0507 > 0.05
  2. X≥13X \geq 13

Part (b)1 mark

  1. The actual probability of a Type I error.0.02160.0216

Part (c)3 marks

  1. P(X≥13∣p=0.5)\mathrm{P}(X \geq 13 \mid p = 0.5)
  2. =0.8192= 0.8192
  3. Power = 1 − P(Type II error).The probability of correctly rejecting H₀ when p=0.5p = 0.5.

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