13 The pre-release material contains information concerning median house prices, recycling rates and employment rates. Fig. 13.1 shows a scatter diagram of recycling rate against employment rate for a random sample of 33 regions.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cea67565-8074-4703-8e1a-09b98e380baf-14_629_1424_397_242}
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\caption{Fig. 13.1}
\end{figure}
The product moment correlation coefficient for this sample is 0.37154 and the associated \(p\)-value is 0.033.
Lee conducts a hypothesis test at the \(5 \%\) level to test whether there is any evidence to suggest there is positive correlation between recycling rate and employment rate. He concludes that there is no evidence to suggest positive correlation because \(0.033 \approx 0\) and \(0.37154 > 0.05\).
- Explain whether Lee's reasoning is correct.
Fig. 13.2 shows a scatter diagram of recycling rate against median house price for a random sample of 33 regions.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cea67565-8074-4703-8e1a-09b98e380baf-14_648_1474_1758_242}
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\caption{Fig. 13.2}
\end{figure}
The product moment correlation coefficient for this sample is - 0.33278 and the associated \(p\)-value is 0.058 .
Fig. 13.3 shows summary statistics for the median house prices for the data in this sample.
\begin{table}[h]
| Statistics |
| \(n\) | 33 |
| Mean | 465467.9697 |
| \(\sigma\) | 201236.1345 |
| \(s\) | 204356.2606 |
| \(\Sigma x\) | 15360443 |
| \(\Sigma x ^ { 2 }\) | 8486161617387 |
| Min | 243500 |
| Q1 | 342500 |
| Median | 410000 |
| Q3 | 521000 |
| Max | 1200000 |
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\caption{Fig. 13.3}
- Use the information in Fig. 13.3 and Fig. 13.2 to show that there are at least two outliers.
- Describe the effect of removing the outliers on