5 A student is investigating immunisation. He wonders if there is any relationship between the percentage of young children who have been given measles vaccine and the percentage who have been given BCG vaccine in various countries.
He takes a random sample of 8 countries and finds the data for the two variables. The spreadsheet in Fig. 5.1 shows the values obtained, together with a scatter diagram which illustrates the data.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{882f9f3c-40d8-4abb-822a-49bd505a33ea-5_910_1653_541_246}
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\caption{Fig. 5.1}
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- The student decides that a test based on Pearson's product moment correlation coefficient is not valid. Explain why he comes to this conclusion.
The student carries out a test based on Spearman’s rank correlation coefficient.
- Calculate the value of Spearman’s rank correlation coefficient.
- Carry out a test based on this coefficient at the \(5 \%\) significance level to investigate whether there is any association between measles and BCG vaccination levels.
The student then decides to investigate the relationship between number of doctors per 1000 people in a country and unemployment rate in that country (unemployment rate is the percentage of the working age population who are not in paid work). He selects a random sample of 6 countries. The spreadsheet in Fig. 5.2 shows the values obtained, together with a scatter diagram which illustrates the data.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{882f9f3c-40d8-4abb-822a-49bd505a33ea-6_776_1649_495_248}
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\caption{Fig. 5.2}
\end{figure} - Use your calculator to write down the equation of the regression line of unemployment rate on doctors per 1000.
- Use the regression line to estimate the unemployment rate for a country with 2.00 doctors per 1000.
- Comment briefly on the reliability of your answer to part (e).
The student decides to add the data for another country with 3.99 doctors per 1000 and unemployment rate 11.42 to his diagram.
- Add this point to the scatter diagram in the Printed Answer Booklet.
- Without doing any further calculations, comment on what difference, if any, including this extra data point would make to the usefulness of a regression line of unemployment rate on doctors per 1000.