2. A researcher believes that there is a linear relationship between daily mean temperature and daily total rainfall. The 7 places in the northern hemisphere from the large data set are used. The mean of the daily mean temperatures, \(t ^ { \circ } \mathrm { C }\), and the mean of the daily total rainfall, \(s \mathrm {~mm}\), for the month of July in 2015 are shown on the scatter diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{565bfa73-8095-4242-80b6-cd47aaff6a31-03_844_1339_497_372}
- With reference to the scatter diagram, explain why a linear regression model may not be suitable for the relationship between \(t\) and s .
(1)
The researcher calculated the product moment correlation coefficient for the 7 places and obtained \(r = 0.658\). - Stating your hypotheses clearly, test at the \(10 \%\) level of significance, whether or not the product moment correlation coefficient for the population is greater than zero.
(3) - Using your knowledge of the large data set, suggest the names of the 2 places labelled \(G\) and \(H\).
(1) - Using your knowledge from the large data set, and with reference to the locations of the two places labelled \(G\) and \(H\), give a reason why these places have the highest temperatures in July.
(2) - Suggest how you could make better use of the large data set to investigate the relationship between daily mean temperature and daily total rainfall.
(1)
(Total 7 marks)