1.1. A random sample of 15 days is taken from the large data set for Perth in June and July 1987.

The scatter diagram in Figure 1 displays the values of two of the variables for these 15 days.

Describe the correlation.

1.2. The variable on the $x$-axis is Daily Mean Temperature measured in °C.

Using your knowledge of the large data set,

(i) suggest which variable is on the $y$-axis,

(ii) state the units that are used in the large data set for this variable.

1.3. Stav believes that there is a correlation between Daily Total Sunshine and Daily Maximum Relative Humidity at Heathrow.

He calculates the product moment correlation coefficient between these two variables for a random sample of 30 days and obtains $r=−0.377$.

Carry out a suitable test to investigate Stav’s belief at a 5% level of significance.

State clearly

• your hypotheses

• your critical value

1.4. On a random day at Heathrow the Daily Maximum Relative Humidity was 97%.

Comment on the number of hours of sunshine you would expect on that day, giving a reason for your answer.