Mathematics · AQA 7357 · Topic O

Statistical hypothesis testing

Hypothesis testing: deciding whether data gives evidence against a claim, for proportions, means and correlation.

  • 3 sub-topics
  • 1 in Year 12, 1 in Year 13
  • 39 practice questions
  • 3 animated lessons
Practice questions (39) Lessons Worksheets All AQA Mathematics topics

What the specification says

Every sub-topic AQA 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. O1The language of hypothesis testingY13
  2. O2Hypothesis test for a binomial proportionY12
  3. O3Hypothesis test for the mean of a normal distributionY13

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Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 39 questions in this topic, free, no account needed.

Statistical hypothesis testing

Easy

Writing hypotheses · Year 12 · 2 marks

A student thinks a coin is biased, without knowing which way.
  1. Write down suitable null and alternative hypotheses.
    (2)
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  1. The null hypothesis is "nothing unusual": the coin is fair.H0:p=0.5\mathrm{H}_0: p = 0.5
  2. Two-tailed, because the bias could be either way.H1:p≠0.5\mathrm{H}_1: p \ne 0.5

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Statistical hypothesis testing

Medium

A two-tailed test · Year 12 · 5 marks

A spinner should land on red with probability 0.4. In 20 spins it lands on red 13 times.
  1. Test at the 5% level whether the probability of red is different from 0.4.
    (5)
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  1. H0:p=0.4\mathrm{H}_0: p = 0.4, H1:p≠0.4\mathrm{H}_1: p \ne 0.4
  2. X∼B(20,0.4)X \sim \mathrm{B}(20, 0.4): P(X≥13)\mathrm{P}(X \ge 13)=1−0.9790{}= 1 - 0.9790=0.0210{}= 0.0210
  3. Split 5% between the two tails.Two-tailed, so compare with 0.025: 0.0210<0.0250.0210 < 0.025
  4. Reject H0\mathrm{H}_0: there is evidence the probability of red is not 0.4

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Statistical hypothesis testing

Hard

Is the coin biased? · Year 12 · 5 marks

Sam thinks a coin is biased towards heads. He tosses it 20 times and gets 15 heads.
  1. Test Sam's claim at the 5% significance level. State your hypotheses clearly.
    (5)
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  1. pp is the probability of heads. The claim is 'towards heads', so the test is one-tailed.H0:p\mathrm{H_0}: p=0.5,{}= 0.5,H1:p>0.5\quad \mathrm{H_1}: p > 0.5
  2. Assume the null hypothesis is true to find how likely the result is.Under H0\mathrm{H_0}, X∼B(20,0.5)X \sim \mathrm{B}(20, 0.5)
  3. Find the probability of a result at least as extreme as the one seen.P(X≥15)\mathrm{P}(X \ge 15)=1−P(X≤14){}= 1 - \mathrm{P}(X \le 14)=0.0207{}= 0.0207
  4. Compare the probability with the significance level.0.0207<0.050.0207 < 0.05, so reject H0\mathrm{H_0}
  5. Always give the conclusion in the context of the question, without certainty.There is evidence that the coin is biased towards heads.

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