OCR MEI AS Paper 2 2021 November — Question 9 5 marks

Exam BoardOCR MEI
ModuleAS Paper 2 (AS Paper 2)
Year2021
SessionNovember
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBivariate data
TypeHypothesis test for correlation
DifficultyModerate -0.5 This is a straightforward AS-level statistics question requiring interpretation of sampling methods and basic understanding of correlation hypothesis testing. Part (a) involves simple reasoning about data sources (checking if cities match pre-release material), while the remaining parts likely involve standard procedures for testing correlation with given data. The question requires minimal calculation and focuses on understanding concepts rather than complex problem-solving, making it slightly easier than average for AS-level.
Spec2.01d Select/critique sampling: in context2.02c Scatter diagrams and regression lines
9 Arun, Beth and Charlie are investigating whether there is any association between death rate per 1000 and physician density per 1000. They each collect a random sample of size 10. Arun's sample is shown in Fig.9.1. \begin{table}[h]
death rate per 1000physician density per 1000
Canberra7.23.62
Dhaka5.30.49
Brasilia6.82.23
Yaounde9.30.08
Zagreb12.53.08
Tehran5.41.16
Rome10.74.14
Tripoli3.82.09
Oslo7.94.51
Abuja9.70.35
\captionsetup{labelformat=empty} \caption{Fig. 9.1}
\end{table}
  1. Explain whether or not Arun collected his data from the pre-release material, or whether it is not possible to say. Beth and Charlie collected their samples from the pre-release material. Each of them drew a scatter diagram for their samples. The samples and scatter diagrams are shown in Figs. 9.2 and 9.3.
    Beth's sampledeath rate per 1000physician density per 1000
    Sudan6.70.41
    Cambodia7.40.17
    Gabon6.20.36
    Seychelles70.95
    Mexico5.42.25
    Kuwait2.32.58
    Haiti7.50.23
    Maldives41.04
    Nauru5.91.24
    Jordan3.42.34
    \includegraphics[max width=\textwidth, alt={}]{2b9ce212-84e2-4817-be94-98e2adff12a3-08_545_1024_340_918}
    \begin{table}[h]
    Charlie's sampledeath rate per 1000physician density per 1000
    Vanuata40.17
    Solomon Islands3.80.2
    N. Mariana Islands4.90.36
    Nauru5.91.24
    United Kingdom9.42.81
    Portugal10.63.34
    North Macedonia9.62.87
    Faroe Islands8.82.62
    Bulgaria14.53.99
    St. Kitts and Nevis7.22.52
    \captionsetup{labelformat=empty} \caption{Fig. 9.3}
    \end{table} \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Fig. 9.2} \includegraphics[alt={},max width=\textwidth]{2b9ce212-84e2-4817-be94-98e2adff12a3-08_572_899_1400_1041}
    \end{figure} Arun states that Charlie's sample and Beth's sample cannot both be random for the following reasons.
    Kofi collects a sample of 10 African countries and 10 European countries. The scatter diagram for his results is shown in Fig. 9.4. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{2b9ce212-84e2-4817-be94-98e2adff12a3-09_485_903_902_260} \captionsetup{labelformat=empty} \caption{Fig. 9.4}
    \end{figure}
  2. On the copy of Fig. 9.4 in the Printed Answer Booklet, use your knowledge of the pre-release material to identify the points representing the 10 European countries, justifying your choice.
Question 9:
Part (a):
AnswerMarks Guidance
AnswerMark Guidance
The sample is not from the pre-release material because Arun has data from capital cities. The pre-release material only has data for countriesB1
[1]
Part (b):
AnswerMarks Guidance
AnswerMark Guidance
It is possible for the same value to be selected in two different random samplesB1
Different samples (especially when small) might lead to different conclusions being madeB1
So there is no evidence to suggest Arun's statement is correctB1
[3]
Part (c):
AnswerMarks Guidance
AnswerMark Guidance
Scatter diagram plottedB1
Many African countries have a lower physician density (and often have a high death rate)B1 OR European countries generally have a higher physician density (and often have a low death rate)
[1] 
## Question 9:

### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| The sample is not from the pre-release material because Arun has data from capital cities. The pre-release material only has data for countries | B1 | |
| **[1]** | | |

### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| It is possible for the same value to be selected in two different random samples | B1 | |
| Different samples (especially when small) might lead to different conclusions being made | B1 | |
| So there is no evidence to suggest Arun's statement is correct | B1 | |
| **[3]** | | |

### Part (c):
| Answer | Mark | Guidance |
|--------|------|----------|
| Scatter diagram plotted | B1 | |
| Many African countries have a lower physician density (and often have a high death rate) | B1 | OR European countries generally have a higher physician density (and often have a low death rate) |
| **[1]** | | |

---
9 Arun, Beth and Charlie are investigating whether there is any association between death rate per 1000 and physician density per 1000. They each collect a random sample of size 10.

Arun's sample is shown in Fig.9.1.

\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
 & death rate per 1000 & physician density per 1000 \\
\hline
Canberra & 7.2 & 3.62 \\
\hline
Dhaka & 5.3 & 0.49 \\
\hline
Brasilia & 6.8 & 2.23 \\
\hline
Yaounde & 9.3 & 0.08 \\
\hline
Zagreb & 12.5 & 3.08 \\
\hline
Tehran & 5.4 & 1.16 \\
\hline
Rome & 10.7 & 4.14 \\
\hline
Tripoli & 3.8 & 2.09 \\
\hline
Oslo & 7.9 & 4.51 \\
\hline
Abuja & 9.7 & 0.35 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 9.1}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Explain whether or not Arun collected his data from the pre-release material, or whether it is not possible to say.

Beth and Charlie collected their samples from the pre-release material. Each of them drew a scatter diagram for their samples. The samples and scatter diagrams are shown in Figs. 9.2 and 9.3.

\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Beth's sample & death rate per 1000 & physician density per 1000 \\
\hline
Sudan & 6.7 & 0.41 \\
\hline
Cambodia & 7.4 & 0.17 \\
\hline
Gabon & 6.2 & 0.36 \\
\hline
Seychelles & 7 & 0.95 \\
\hline
Mexico & 5.4 & 2.25 \\
\hline
Kuwait & 2.3 & 2.58 \\
\hline
Haiti & 7.5 & 0.23 \\
\hline
Maldives & 4 & 1.04 \\
\hline
Nauru & 5.9 & 1.24 \\
\hline
Jordan & 3.4 & 2.34 \\
\hline
\end{tabular}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth, alt={}]{2b9ce212-84e2-4817-be94-98e2adff12a3-08_545_1024_340_918}
\end{center}

\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Charlie's sample & death rate per 1000 & physician density per 1000 \\
\hline
Vanuata & 4 & 0.17 \\
\hline
Solomon Islands & 3.8 & 0.2 \\
\hline
N. Mariana Islands & 4.9 & 0.36 \\
\hline
Nauru & 5.9 & 1.24 \\
\hline
United Kingdom & 9.4 & 2.81 \\
\hline
Portugal & 10.6 & 3.34 \\
\hline
North Macedonia & 9.6 & 2.87 \\
\hline
Faroe Islands & 8.8 & 2.62 \\
\hline
Bulgaria & 14.5 & 3.99 \\
\hline
St. Kitts and Nevis & 7.2 & 2.52 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 9.3}
\end{center}
\end{table}

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Fig. 9.2}
  \includegraphics[alt={},max width=\textwidth]{2b9ce212-84e2-4817-be94-98e2adff12a3-08_572_899_1400_1041}
\end{center}
\end{figure}

Arun states that Charlie's sample and Beth's sample cannot both be random for the following reasons.

\begin{itemize}
  \item Both samples include Nauru - there should not be any common values.
  \item Beth's diagram suggests a negative association between death rate and physician density, whereas Charlie's diagram suggests a positive association. If both samples are random the same relationship would be suggested.
\item - Explain whether Arun's reasons are valid.
  \item State whether or not Arun is correct, or whether it is not possible to say.
\end{itemize}

Kofi collects a sample of 10 African countries and 10 European countries. The scatter diagram for his results is shown in Fig. 9.4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{2b9ce212-84e2-4817-be94-98e2adff12a3-09_485_903_902_260}
\captionsetup{labelformat=empty}
\caption{Fig. 9.4}
\end{center}
\end{figure}
\item On the copy of Fig. 9.4 in the Printed Answer Booklet, use your knowledge of the pre-release material to identify the points representing the 10 European countries, justifying your choice.
\end{enumerate}

\hfill \mbox{\textit{OCR MEI AS Paper 2 2021 Q9 [5]}}
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