Question 1 - A-Level Maths

AQA S3 2012 June — Question 1 6 marks

Exam Board	AQA
Module	S3 (Statistics 3)
Year	2012
Session	June
Marks	6
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Hypothesis test of Pearson’s product-moment correlation coefficient
Type	Calculate PMCC from summary statistics
Difficulty	Moderate -0.8 This is a straightforward calculation of PMCC from summary statistics using the standard formula. It requires only direct substitution into a formula that students will have memorised and practised extensively, with no problem-solving or interpretation required beyond basic arithmetic.
Spec	5.08a Pearson correlation: calculate pmcc 5.08d Hypothesis test: Pearson correlation 5.09a Dependent/independent variables 5.09c Calculate regression line

1 A wildlife expert measured the neck lengths, \(x\) metres, and the tail lengths, \(y\) metres, of a sample of 12 mature male giraffes as part of a study into their physical characteristics. The results are shown in the table.

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Question 1:

Part (a)

Answer	Marks	Guidance
Answer	Mark	Guidance
\(r = 0.882\) (accept awrt 0.882)	B2	B1 for correct method seen with wrong answer; B2 for correct answer

Part (b)

Answer	Marks	Guidance
Answer	Mark	Guidance
\(H_0: \rho = 0\), \(H_1: \rho > 0\)	B1	Both hypotheses correct using \(\rho\)
Critical value = 0.6429 (one-tailed, 1%, \(n=12\))	B1	Correct critical value
\(0.882 > 0.6429\), so reject \(H_0\)	M1	Correct comparison leading to conclusion
There is evidence of a positive correlation between neck length and tail length of mature male giraffes	A1	Conclusion in context

# Question 1:

## Part (a)

| Answer | Mark | Guidance |
|--------|------|----------|
| $r = 0.882$ (accept awrt 0.882) | B2 | B1 for correct method seen with wrong answer; B2 for correct answer |

## Part (b)

| Answer | Mark | Guidance |
|--------|------|----------|
| $H_0: \rho = 0$, $H_1: \rho > 0$ | B1 | Both hypotheses correct using $\rho$ |
| Critical value = 0.6429 (one-tailed, 1%, $n=12$) | B1 | Correct critical value |
| $0.882 > 0.6429$, so reject $H_0$ | M1 | Correct comparison leading to conclusion |
| There is evidence of a positive correlation between neck length and tail length of mature male giraffes | A1 | Conclusion in context |

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1 A wildlife expert measured the neck lengths, $x$ metres, and the tail lengths, $y$ metres, of a sample of 12 mature male giraffes as part of a study into their physical characteristics. The results are shown in the table.

\hfill \mbox{\textit{AQA S3 2012 Q1 [6]}}

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Q1 6 Q2 7 Q3 14 Q4 6 Q5 10 Q6 17 Q7 15