| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2022 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Distinguish dependent and independent variables |
| Difficulty | Moderate -0.8 This is a straightforward bivariate data question testing basic concepts: identifying independent/dependent variables, calculating PMCC from summary statistics using a standard formula, conducting a routine hypothesis test, and recognizing correlation is invariant under linear transformations. All parts are standard textbook exercises requiring recall and direct application of formulas with no problem-solving or novel insight needed. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (a) | Independent (and no others) |
| (b) | 0.713 BC | B2 |
| [2] | 1.1 | |
| 1.1 | SC: If B0, give B1 for any 2 of 16.02, 14.24, | |
| 10.77, or any 2 of 192.25, 170.9, 129.25 seen | e.g. 769/4, 2051/12, 517/4 | |
| (c) | (i) | “More computer failures when |
| Answer | Marks | Guidance |
|---|---|---|
| lower temperatures” | B1 | |
| [1] | 2.4 | Oe |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | (ii) | H = 0, H : > 0 |
| Answer | Marks |
|---|---|
| and number of failures | B2 |
| Answer | Marks |
|---|---|
| [6] | 1.1 |
| Answer | Marks |
|---|---|
| 2.2b | Treat association and correlation as equivalent |
| Answer | Marks |
|---|---|
| 0.4973 or 0.5760; contextualised, not too definite | See Appendix for exemplars |
| Answer | Marks | Guidance |
|---|---|---|
| (d) | 0.713 | B1ft |
| [1] | 1.2 | Their (b). Allow “unchanged”, etc. |
Question 2:
2 | (a) | Independent (and no others) | B1 | 2.5 | Fully correct only
(b) | 0.713 BC | B2
[2] | 1.1
1.1 | SC: If B0, give B1 for any 2 of 16.02, 14.24,
10.77, or any 2 of 192.25, 170.9, 129.25 seen | e.g. 769/4, 2051/12, 517/4
(c) | (i) | “More computer failures when
temperatures are higher”, rather than
“number of failures is related to higher or
lower temperatures” | B1
[1] | 2.4 | Oe
Allow “Looking for positive correlation”, etc
(c) | (ii) | H = 0, H : > 0
0: 1
where is the population PMCC between
temperature and number of failures
CV = 0.6581
0.713 > 0.6581
Reject H . Significant evidence of
0
(positive) correlation between temperature
and number of failures | B2
B1
B1ft
M1ft
A1ft
[6] | 1.1
2.5
1.1
1.1
1.1
2.2b | Treat association and correlation as equivalent
One error, e.g. 2-tail, or not defined: B1
(allow H : 0). Allow omission of “population”
0
(or “true”) or of context, but not of both
Correct CV, or p = 0.00462
Explicit comparison, their r, allow “pmcc > CV”
FT on their r, needs 0.6581, 0.6851, 0.7079,
0.4973 or 0.5760; contextualised, not too definite | See Appendix for exemplars
Verbal, e.g. H : no correlation between
0
temperature and number of failures, H :
1
positive correlation: max B1, one error B0
Their CV must be from tables for r or r
s
If inconsistent with comparison, M0A0
Not “insufficient evidence of no correlation
between …”
(d) | 0.713 | B1ft
[1] | 1.2 | Their (b). Allow “unchanged”, etc.2 The directors of a large company believe that there are more computer failures in the Head Office when temperatures are higher. They obtain data for the Head Office for the maximum temperature, $T ^ { \circ } \mathrm { C }$, and the number of computer failures, $X$, on each of 12 randomly chosen days.
\begin{enumerate}[label=(\alph*)]
\item State which of the following words can be applied to $T$.
Dependent Independent Controlled Response
The data is summarised as follows.\\
$n = 12 \quad \sum t = 261 \quad \sum x = 41 \quad \sum t ^ { 2 } = 5869 \quad \sum x ^ { 2 } = 311 \quad \sum \mathrm { tx } = 1021$
\item Calculate the value of the product moment correlation coefficient $r$.
\item The directors wish to investigate their belief using a significance test at the $1 \%$ level.
\begin{enumerate}[label=(\roman*)]
\item Explain why a 1-tail test is appropriate in this situation.
\item Carry out the test.
\end{enumerate}\item One of the directors prefers the temperatures to be given in Fahrenheit ( ${ } ^ { \circ } \mathrm { F }$ ), rather than Centigrade ( ${ } ^ { \circ } \mathrm { C }$ ). The relationship between F and C is $\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32$.\\
State the value of $r$ that would result from using temperatures in Fahrenheit in the calculation.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2022 Q2 [11]}}