CAIE FP2 2013 June — Question 5 4 marks

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2013
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicHypothesis test of Pearson’s product-moment correlation coefficient
TypeOne-tailed test for negative correlation
DifficultyStandard +0.3 This is a straightforward application of a standard hypothesis test for correlation with clear parameters given (n=12, r=-0.456, α=0.05). Students need only state hypotheses, find the critical value from tables, compare, and conclude. While it's Further Maths content, it requires minimal steps and is a textbook procedure with no problem-solving or conceptual challenges beyond basic statistical testing.
Spec5.08d Hypothesis test: Pearson correlation
5 For a random sample of 12 observations of pairs of values \(( x , y )\), the product moment correlation coefficient is - 0.456 . Test, at the \(5 \%\) significance level, whether there is evidence of negative correlation between the variables.
Question 5:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(H_0\): \(\rho = 0\), \(H_1\): \(\rho < 0\)B1 State both hypotheses (B0 if \(r\) not \(\rho\) used)
\(r_{12,\,5\%} = 0.497\)*B1 State or use correct tabular one-tail \(r\) value
Accept \(H_0\) if \(r <\) tabular value
No evidence of negative correlationA1 Correct conclusion (AEF, dep *B1)
Total: 4 marks
## Question 5:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0$: $\rho = 0$, $H_1$: $\rho < 0$ | B1 | State both hypotheses (B0 if $r$ not $\rho$ used) |
| $r_{12,\,5\%} = 0.497$ | *B1 | State or use correct tabular one-tail $r$ value |
| Accept $H_0$ if $|r| <$ tabular value | M1 | Valid method for reaching conclusion |
| No evidence of negative correlation | A1 | Correct conclusion (AEF, dep *B1) |

**Total: 4 marks**

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5 For a random sample of 12 observations of pairs of values $( x , y )$, the product moment correlation coefficient is - 0.456 . Test, at the $5 \%$ significance level, whether there is evidence of negative correlation between the variables.

\hfill \mbox{\textit{CAIE FP2 2013 Q5 [4]}}
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Q1 8 Q2 11 Q3 12 Q4 12 Q5 4 Q6 7 Q7 9 Q8 9 Q9 14 Q10 EITHER Q10 OR