| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2021 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Pearson’s product-moment correlation coefficient |
| Type | One-tailed test for negative correlation |
| Difficulty | Standard +0.3 This is a straightforward hypothesis testing question requiring calculation of Pearson's correlation coefficient from given summary statistics, performing a standard one-tailed test using critical values, and commenting on interpretation. All steps are routine procedures covered in Further Statistics with no novel problem-solving required, though it's slightly above average difficulty due to being Further Maths content. |
| Spec | 2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation2.05e Hypothesis test for normal mean: known variance2.05f Pearson correlation coefficient2.05g Hypothesis test using Pearson's r5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | PMCC = −0.2020 |
| [1] | 1.1 | Allow -0.202 |
| 3 | (b) | Shape of pattern of points in scatter diagram is |
| Answer | Marks |
|---|---|
| be valid | E1 |
| Answer | Marks |
|---|---|
| [2] | 3.5a |
| 2.4 | SC1 for “the data is random on random” if first E1 not |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (c) | H : ρ = 0 |
| Answer | Marks |
|---|---|
| AG) | B1 |
| Answer | Marks |
|---|---|
| [4] | 3.3 |
| Answer | Marks |
|---|---|
| 1.1 | For both hypotheses |
| Answer | Marks |
|---|---|
| Correct conclusion reached www | O |
| Answer | Marks |
|---|---|
| − |
| Answer | Marks |
|---|---|
| − |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (d) | The result of a hypothesis test can never give a certain |
| Answer | Marks |
|---|---|
| to produce a significant result. | E1 |
| Answer | Marks |
|---|---|
| [2] | 2.2a |
| 2.4 | First E1 for statement about uncertainty in hypothesis tests |
Question 3:
3 | (a) | PMCC = −0.2020 | B1
[1] | 1.1 | Allow -0.202
3 | (b) | Shape of pattern of points in scatter diagram is
approximately elliptical
so there is evidence to suggest bivariate Normality in
the population which is required for test using pmcc to
be valid | E1
E1
[2] | 3.5a
2.4 | SC1 for “the data is random on random” if first E1 not
awarded.
3 | (c) | H : ρ = 0
0
H : ρ < 0 (one-tailed test)
1
where ρ is the population product moment correlation
coefficient between daily mean temperature and
electricity consumption
For n = 10, 5% critical value (one tailed) = −0.5494
Since −0.2020 > −0.5494 the result is
not significant (so the null hypothesis is not rejected
AG) | B1
B1
M1
A1
[4] | 3.3
3.4
1.1 | For both hypotheses
For critical value ± 0.5494
For appropriate comparison using their cv leading to a
conclusion.
Correct conclusion reached www | O
r
|−
0.
20
20
|
<
|−
0.
54
94
|
3 | (d) | The result of a hypothesis test can never give a certain
result and so, although the student may be correct, it is
also possible that there is negative correlation, but not
enough negative correlation with such a small sample
to produce a significant result. | E1
E1
[2] | 2.2a
2.4 | First E1 for statement about uncertainty in hypothesis tests
in general or for the student’s overly assertive conclusion
and second E1 for further relevant comment relating to this
particular test/sample.3 A student is investigating the link between temperature (in degrees Celsius) and electricity consumption (in Gigawatt-hours) in the country in which he lives.
The student has read that there is strong negative correlation between daily mean temperature over the whole country and daily electricity consumption during a year. He wonders if this applies to an individual season. He therefore obtains data on the mean temperature and electricity consumption on ten randomly selected days in the summer. The spreadsheet output below shows the data, together with a scatter diagram to illustrate the data.\\
\includegraphics[max width=\textwidth, alt={}, center]{5be067ff-4668-48d6-8ed2-b8dfa3e678f7-3_798_1593_639_251}
\begin{enumerate}[label=(\alph*)]
\item Calculate Pearson's product moment correlation coefficient between daily mean temperature and daily electricity consumption.
The student decides to carry out a hypothesis test to investigate whether there is negative correlation between daily mean temperature and daily electricity consumption during the summer.
\item Explain why the student decides to carry out a test based on Pearson's product moment correlation coefficient.
\item Show that the test at the $5 \%$ significance level does not result in the null hypothesis being rejected.
\item The student concludes that there is no correlation between the variables in the summer months.
Comment on the student's conclusion.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2021 Q3 [9]}}