Moderate -0.8 This is a straightforward calculation of PMCC from given data using the standard formula. While it requires careful arithmetic with summary statistics, it's a routine procedural task with no conceptual difficulty or problem-solving required—easier than the average A-level question which typically involves some multi-step reasoning.
1 A demographer measured the length of the right foot, \(x\) millimetres, and the length of the right hand, \(y\) millimetres, of each of a sample of 12 males aged between 19 years and 25 years. The results are given in the table.
Critical value at 1% significance, \(n=12\), one-tail: \(cv = 0.6429\)
B1
Correct critical value
Since \(0.887 > 0.6429\), reject \(H_0\)
M1
Correct comparison
There is sufficient evidence at the 1% level of a positive correlation between the length of the right foot and length of the right hand
A1
Conclusion in context
# Question 1:
## Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $r = \frac{S_{xy}}{\sqrt{S_{xx} \cdot S_{yy}}} = \frac{3095}{\sqrt{7410 \times 1642}}$ | M1 | Correct formula with values substituted |
| $r = \frac{3095}{\sqrt{12,167,220}} = \frac{3095}{3488.2...} = 0.8873...$ awrt $0.887$ | A1 | |
## Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $H_0: \rho = 0$, $H_1: \rho > 0$ | B1 | Both hypotheses correct with $\rho$ |
| Critical value at 1% significance, $n=12$, one-tail: $cv = 0.6429$ | B1 | Correct critical value |
| Since $0.887 > 0.6429$, reject $H_0$ | M1 | Correct comparison |
| There is sufficient evidence at the 1% level of a positive correlation between the length of the right foot and length of the right hand | A1 | Conclusion in context |
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1 A demographer measured the length of the right foot, $x$ millimetres, and the length of the right hand, $y$ millimetres, of each of a sample of 12 males aged between 19 years and 25 years. The results are given in the table.
\hfill \mbox{\textit{AQA S3 2015 Q1 [6]}}