- A meteorologist believes that there is a relationship between the daily mean windspeed, \(w \mathrm { kn }\), and the daily mean temperature, \(t ^ { \circ } \mathrm { C }\). A random sample of 9 consecutive days is taken from past records from a town in the UK in July and the relevant data is given in the table below.
| \(\boldsymbol { t }\) | 13.3 | 16.2 | 15.7 | 16.6 | 16.3 | 16.4 | 19.3 | 17.1 | 13.2 |
| \(\boldsymbol { w }\) | 7 | 11 | 8 | 11 | 13 | 8 | 15 | 10 | 11 |
The meteorologist calculated the product moment correlation coefficient for the 9 days and obtained \(r = 0.609\)
- Explain why a linear regression model based on these data is unreliable on a day when the mean temperature is \(24 ^ { \circ } \mathrm { C }\)
- State what is measured by the product moment correlation coefficient.
- Stating your hypotheses clearly test, at the \(5 \%\) significance level, whether or not the product moment correlation coefficient for the population is greater than zero.
Using the same 9 days a location from the large data set gave \(\bar { t } = 27.2\) and \(\bar { w } = 3.5\)
- Using your knowledge of the large data set, suggest, giving your reason, the location that gave rise to these statistics.