Standard +0.3 This is a straightforward application of the Pearson's correlation coefficient hypothesis test with all summary statistics provided. Students must calculate r using the standard formula, state hypotheses for a one-tailed test, and compare with critical values from tables. While it's a Further Maths topic (making it slightly above average), the question requires only direct substitution into a formula and table lookup with no conceptual complications or multi-step reasoning.
2 A shopper estimates the cost, \(\pounds X\) per item, of each of 12 items in a supermarket. The shopper's estimates are compared with the actual cost, \(\pounds Y\) per item, of each item. The results are summarised as follows.
\(n = 12\)
\(\sum x = 399\)
\(\sum y = 623.88\)
\(\sum x ^ { 2 } = 28127\)
\(\sum y ^ { 2 } = 116509.0212\)
\(\sum x y = 45006.01\)
Test at the 1\% significance level whether the shopper's estimates are positively correlated with the actual cost of the items.
B1 if one error or if \(\rho\) not defined as population parameter
where \(\rho\) is the population correlation coefficient
B1
\(r_\text{crit} = 0.6581\)
B1
Seen. Allow 0.658
Reject \(H_0\). There is significant evidence of positive correlation between the taster's estimates and the actual price.
M1ft
Correct first conclusion
A1ft
Contextualised, not too definite. FT on their \(r\) but not their CV
[7]
## Question 2:
$r = 0.686(41)$ | **M1** | Evidence for correct method (e.g. correct value)
| **A1** | Correct value
$H_0: \rho = 0,\ H_1: \rho > 0$ | **B1** | B1 if one error or if $\rho$ not defined as population parameter
where $\rho$ is the population correlation coefficient | **B1** |
$r_\text{crit} = 0.6581$ | **B1** | Seen. Allow 0.658
Reject $H_0$. There is significant evidence of positive correlation between the taster's estimates and the actual price. | **M1ft** | Correct first conclusion
| **A1ft** | Contextualised, not too definite. FT on their $r$ but not their CV
[7]
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2 A shopper estimates the cost, $\pounds X$ per item, of each of 12 items in a supermarket. The shopper's estimates are compared with the actual cost, $\pounds Y$ per item, of each item. The results are summarised as follows.\\
$n = 12$\\
$\sum x = 399$\\
$\sum y = 623.88$\\
$\sum x ^ { 2 } = 28127$\\
$\sum y ^ { 2 } = 116509.0212$\\
$\sum x y = 45006.01$\\
Test at the 1\% significance level whether the shopper's estimates are positively correlated with the actual cost of the items.
\hfill \mbox{\textit{OCR Further Statistics AS 2021 Q2 [7]}}