| Exam Board | OCR |
|---|---|
| Module | Further Statistics AS (Further Statistics AS) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Pearson’s product-moment correlation coefficient |
| Type | Effect of coding on correlation |
| Difficulty | Standard +0.3 This is a straightforward correlation and regression question requiring standard calculations (regression line equation, hypothesis test for correlation coefficient) with mostly routine procedures. The conceptual twist about correlation vs causation in part (iii)(b) and the unit invariance in part (ii) add minimal difficulty. The correlation coefficient is given, simplifying the hypothesis test to a table lookup with n=10. |
| Spec | 2.02e Correlation does not imply causation5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.09c Calculate regression line |
| \(x\) | 9.3 | 9.7 | 9.7 | 9.7 | 9.9 | 10.2 | 10.5 | 11.0 | 10.6 | 10.6 |
| \(y\) | 480 | 501 | 540 | 552 | 547 | 622 | 655 | 701 | 712 | 708 |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | (i) | y(cid:32)157x(cid:16)988 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 3.3 | n |
| Answer | Marks |
|---|---|
| All correct including letters | BC |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | (ii) | No; r is unaffected by linear coding |
| [1] | 2.3 | e |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | (iii) | (a) |
| Answer | Marks |
|---|---|
| civil engineering doctorates awarded. | cB2 |
| Answer | Marks |
|---|---|
| [6] | i |
| Answer | Marks |
|---|---|
| 2.2b | Hypotheses correctly stated |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | (iii) | (b) |
| [1] | 3.5b | Or: “there may be another factor |
Question 8:
8 | (i) | y(cid:32)157x(cid:16)988 | B1
B1
[2] | 1.1
3.3 | n
Either coefficient correct to 3 s.f.
All correct including letters | BC
(cid:62)y(cid:32)157.11x(cid:16)988.15(cid:64)
8 | (ii) | No; r is unaffected by linear coding | E1
[1] | 2.3 | e
mNeeds both “no” and “linear”
seen, and no wrong or irrelevant
statements
8 | (iii) | (a) | H :(cid:85)(cid:32)0
0
H :(cid:85)(cid:122)0 where (cid:85) is the population correlation
1
coefficient
CV0.5494
p
0.9586(cid:33)0.5494
S
Reject H
0
Significant evidence of correlation between
consumption of mozzarella cheese and number of
civil engineering doctorates awarded. | cB2
e
B1
M1
M1
A1
[6] | i
1.1
2.5
3.4
1.1
1.1
2.2b | Hypotheses correctly stated
B1 if no symbol used
Correct critical value seen
Explicit comparison
Correct first conclusion
Contextualised, acknowledge
uncertainty
8 | (iii) | (b) | No, correlation does not imply causality | E1
[1] | 3.5b | Or: “there may be another factor
that influences both”
PPMMTT
Y532 Mark Scheme June 20XX
Assessment Objectives (AO) Grid
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M = Modelling
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PPMMTT
Y532 Mark Scheme June 20XX
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PPMMTT
AS Level Further Mathematics A
Y532 Statistics
Printed Answer Booklet
Date – Morning/Afternoon
Time allowed: 1 hour 15 minutes
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© OCR 2017 Y532
The following table gives the mean per capita consumption of mozzarella cheese per annum, $x$ pounds, and the number of civil engineering doctorates awarded, $y$, in the United States in each of 10 years.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
$x$ & 9.3 & 9.7 & 9.7 & 9.7 & 9.9 & 10.2 & 10.5 & 11.0 & 10.6 & 10.6 \\
\hline
$y$ & 480 & 501 & 540 & 552 & 547 & 622 & 655 & 701 & 712 & 708 \\
\hline
\end{tabular}
source: www.tylervigen.com
\begin{enumerate}[label=(\roman*)]
\item Find the equation of the regression line of $y$ on $x$. [2]
\end{enumerate}
You are given that the product moment correlation coefficient is 0.959.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Explain whether this value would be different if $x$ is measured in kilograms instead of pounds. [1]
\end{enumerate}
It is desired to carry out a hypothesis test to investigate whether there is correlation between these two variables.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Assume that the data is a random sample of all years.
\begin{enumerate}[label=(\alph*)]
\item Carry out the test at the 10\% significance level. [6]
\item Explain whether your conclusion suggests that manufacturers of mozzarella cheese could increase consumption by sponsoring doctoral candidates in civil engineering. [1]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics AS Q8 [10]}}