Spearman's rank correlation Problem set B Answers

0.738

0.907

1. (a) Critic 1: 3, 5, 7, 1, 8, 4, 2, 6; Critic 2: 4, 5, 6, 2, 8, 3, 1, 7
2. (b) 0.929

1. (a) H0: there is no correlation between hours of sunshine and ice cream sales. H1: there is a positive correlation between hours of sunshine and ice cream sales.
2. (b) 0.857
3. (c) There is sufficient evidence, at the 5% significance level, of a positive correlation between hours of sunshine and ice cream sales.

1. (a) H0: there is no correlation between days absent and exam mark. H1: there is a negative correlation between days absent and exam mark.
2. (b) −0.905
3. (c) There is sufficient evidence, at the 10% significance level, of a negative correlation between days absent and exam mark.

1. (a) −0.950
2. (b) There is sufficient evidence, at the 5% significance level, of a correlation between speed and fuel economy.

1. (a) 0.771
2. (b) There is insufficient evidence, at the 5% significance level, that the two coaches tend to agree.

1. (a) r_s = −0.952: strong negative correlation: people who exercise more tend to have lower blood pressure.
2. (b) No. r_s is not exactly −1, so the ranks are not perfectly reversed: at least one person exercises more than another but has higher blood pressure. The data show a tendency, not 'always'.

1. (a) r increases (closer to 1)
2. (b) r_s stays the same (0.964)
3. (c) r_s does not change

1. (a) 1
2. (b) r_s measures how well the ranks agree, whatever the shape. The ranks are in exactly the same order, so r_s = 1. Pearson's r only measures straight-line correlation, and these points lie on a curve, so r < 1.