OCR S4 2015 June — Question 6 9 marks

Exam BoardOCR
ModuleS4 (Statistics 4)
Year2015
SessionJune
Marks9
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Mark schemeDownload PDF ↗
TopicWilcoxon tests
TypeWilcoxon rank-sum test (Mann-Whitney U test)
DifficultyModerate -0.8 This is a straightforward application of the Wilcoxon rank-sum test with all necessary information provided (sample sizes, rank sum, significance level). It requires only routine calculation of the test statistic, comparison with critical values from tables, and stating a conclusion—no problem-solving insight or complex reasoning needed. The mechanical nature and single-step process make it easier than average A-level questions.
Spec5.07d Paired vs two-sample: selection
6 In a two-tail Wilcoxon rank-sum test, the sample sizes are 13 and 15. The sum of the ranks for the sample of size 13 is 135 . Carry out the test at the \(5 \%\) level of significance.
AnswerMarks Guidance
Wilcoxon rank-sum test performed.M1 M1 M1 M1 M1 M1 M1 M1 M1 A1 Method: Sample sizes \(n_1 = 13\), \(n_2 = 15\). Sum of ranks for sample 1 is \(S_1 = 135\). Under null hypothesis, \(E(S_1) = \frac{n_1(n_1 + n_2 + 1)}{2} = \frac{13 \times 29}{2} = 188.5\). \(\text{Var}(S_1) = \frac{n_1 n_2(n_1 + n_2 + 1)}{12} = \frac{13 \times 15 \times 29}{12} = 470.8\). \(\sigma = 21.7\). Test statistic: \(z = \frac{135 - 188.5}{21.7} = -2.46\). Two-tailed test at 5% gives critical values \(\pm 1.96\). Since \( 
| Wilcoxon rank-sum test performed. | M1 M1 M1 M1 M1 M1 M1 M1 M1 A1 | **Method:** Sample sizes $n_1 = 13$, $n_2 = 15$. Sum of ranks for sample 1 is $S_1 = 135$. Under null hypothesis, $E(S_1) = \frac{n_1(n_1 + n_2 + 1)}{2} = \frac{13 \times 29}{2} = 188.5$. $\text{Var}(S_1) = \frac{n_1 n_2(n_1 + n_2 + 1)}{12} = \frac{13 \times 15 \times 29}{12} = 470.8$. $\sigma = 21.7$. Test statistic: $z = \frac{135 - 188.5}{21.7} = -2.46$. Two-tailed test at 5% gives critical values $\pm 1.96$. Since $|-2.46| > 1.96$, reject the null hypothesis at the 5% significance level |
6 In a two-tail Wilcoxon rank-sum test, the sample sizes are 13 and 15. The sum of the ranks for the sample of size 13 is 135 . Carry out the test at the $5 \%$ level of significance.

\hfill \mbox{\textit{OCR S4 2015 Q6 [9]}}
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