1.1. Medhi is a meteorologist investigating the weather in Heathrow and claims that there is negative correlation between the daily total rainfall, $f$ mm, and daily total sunshine, $s$ hours.

Medhi decides to use the large data set to investigate this claim and forms a sample using all the days in June 2015 relating to Heathrow.

Some values for the daily total rainfall, $f$ mm, are labelled as 'tr'. Using your knowledge of the large data set, state the range of values Medhi could assign to these values.

1.2. Medhi uses all the days in June 2015 as a sample and calculates the product moment correlation coefficient to be $r=-0.2659$.

Carry out a suitable test at the 5% level of significance to investigate Medhi's claim. You should:

• state your hypotheses clearly

• state the critical value used

1.3. Medhi uses this data to calculate the equation for the regression line of $f$ on $s$. He plans to use the regression line to estimate the amount of rainfall there will be in Heathrow during a day in December.

Give two reasons why this is unlikely to produce a reliable estimate.