Practise carrying out and interpreting single-sample non-parametric tests of a population median with Further Mathematics AS questions and mark schemes.
Use a Wilcoxon signed-rank test to test whether the average pollution level in the river is more than 6.00. Use a 5% significance level.
H0: population median is 6.00,H1: population median is greater than 6.00
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Both hypotheses stated
Calculate deviations and resulting signed ranks
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Devs & -0.38 & -0.27 & 0.55 & 0.81 & 0.10 & -0.25 & -0.13 & 0.47 & -0.14 & 0.26 & 0.99 & -0.09
Rank & -8 & -7 & 10 & 11 & 2 & -5 & -3 & 9 & -4 & 6 & 12 & -1
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Test statistic T=8+7+5+3+4+1=28
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Compare with correct critical value 17
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Conclusion: accept H0;
insufficient evidence that the median is greater than
6.00
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A1FT
Conclusion to be stated in context, not just 'not
significant';
follow through their value of T
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