3. (a) Describe when you would use Spearman's rank correlation coefficient rather than the product moment correlation coefficient to measure the strength of the relationship between two variables.
(1)
A shop sells sunglasses and ice cream. For one week in the summer the shopkeeper ranked the daily sales of ice cream and sunglasses. The ranks are shown in the table below.
| Sun | Mon | Tues | Weds | Thurs | Fri | Sat |
| Ice cream | 6 | 4 | 7 | 5 | 3 | 2 | 1 |
| Sunglasses | 6 | 5 | 7 | 2 | 3 | 4 | 1 |
(b) Calculate Spearman's rank correlation coefficient for these data.
(c) Test, at the \(5 \%\) level of significance, whether or not there is a positive correlation between sales of ice cream and sales of sunglasses. State your hypotheses clearly.
The shopkeeper calculates the product moment correlation coefficient from his raw data and finds \(r = 0.65\)
(d) Using this new coefficient, test, at the \(5 \%\) level of significance, whether or not there is a positive correlation between sales of ice cream and sales of sunglasses.
(e) Using your answers to part (c) and part (d), comment on the nature of the relationship between sales of sunglasses and sales of ice cream.