4 Two magazines give numerical ratings to hi-fi systems. Li wishes to test whether there is agreement between the opinions of the magazines. Li chooses a random sample of 5 hi -fi systems and looks up the ratings given by the two magazines. The results are shown in the table.

1. Give a reason why Li might choose to use a test based on Spearman's rank correlation coefficient rather than on Pearson’s product-moment correlation coefficient.
2. Calculate the value of Spearman's rank correlation coefficient for the data.
3. Use your answer to part (b) to carry out a hypothesis test at the \(5 \%\) significance level.
4. The value of Spearman's rank correlation coefficient between the ratings given by magazine I and by a third magazine, magazine III, has the same numerical value as the answer to part (b) but with the sign changed. In the Printed Answer Booklet, complete the table showing the rankings given by magazine III.