OCR S4 2018 June — Question 1 5 marks

Exam BoardOCR
ModuleS4 (Statistics 4)
Year2018
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicWilcoxon tests
TypeWilcoxon signed-rank test (single sample)
DifficultyModerate -0.5 This is a straightforward application of the Wilcoxon signed-rank test requiring only table lookup and comparison. The student must compare T=162 against the critical value for n=32 at 5% significance (one-tailed), which is routine procedure with no problem-solving or conceptual challenge beyond basic hypothesis test mechanics.
Spec5.07b Sign test: and Wilcoxon signed-rank5.07c Single-sample tests

1 A Wilcoxon signed-rank test is carried out at the \(5 \%\) level of significance on a random sample of size 32 . The hypotheses are \(\mathrm { H } _ { 0 } : m = m _ { 0 } , \mathrm { H } _ { 1 } : m < m _ { 0 }\) where \(m\) is the population median and \(m _ { 0 }\) is a specific numerical value. The value obtained for the test statistic \(T\) is 162 . Find the outcome of the test.

Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(\bar{x} = \frac{\sum x}{n}\)M1 Method for mean
\(= 4.35\)A1 cao
etc.
Mark Scheme 4735/01 June 2018
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Mean \(= 264\), Variance \(= 2860\)B1B1 May be implied
\(\frac{162 + 0.5 - 264}{\sqrt{2860}}\)M1 Allow missing CC for M1
\(= -1.898\) or \(p = 0.029\)A1
\(< -1.645\), or \(2.9\% < 5\%\) reject \(H_0\) (result is significant)B1ft, [5] ft incorrect TS, NOT CV
**Question 1:**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\bar{x} = \frac{\sum x}{n}$ | M1 | Method for mean |
| $= 4.35$ | A1 | cao |

etc.

# Mark Scheme 4735/01 June 2018

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## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Mean $= 264$, Variance $= 2860$ | B1B1 | May be implied |
| $\frac{162 + 0.5 - 264}{\sqrt{2860}}$ | M1 | Allow missing CC for M1 |
| $= -1.898$ or $p = 0.029$ | A1 | |
| $< -1.645$, or $2.9\% < 5\%$ reject $H_0$ (result is significant) | B1ft, [5] | ft incorrect TS, NOT CV |

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1 A Wilcoxon signed-rank test is carried out at the $5 \%$ level of significance on a random sample of size 32 . The hypotheses are $\mathrm { H } _ { 0 } : m = m _ { 0 } , \mathrm { H } _ { 1 } : m < m _ { 0 }$ where $m$ is the population median and $m _ { 0 }$ is a specific numerical value. The value obtained for the test statistic $T$ is 162 . Find the outcome of the test.

\hfill \mbox{\textit{OCR S4 2018 Q1 [5]}}