Spearman's rank correlation Problem set A Answers

−0.976

0.864

1. (a) Judge 1: 4, 2, 5, 8, 1, 7, 6, 3; Judge 2: 3, 1, 4, 6, 2, 8, 7, 5
2. (b) 0.833

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

1. (a) H0: there is no correlation between hours of television and test mark. H1: there is a negative correlation between hours of television and test mark.
2. (b) −0.952
3. (c) There is sufficient evidence, at the 10% significance level, of a negative correlation between hours of television and test mark.

1. (a) 0.933
2. (b) There is sufficient evidence, at the 5% significance level, of a correlation between age and height.

1. (a) 0.783
2. (b) There is insufficient evidence, at the 5% significance level, that the two judges tend to agree.

1. (a) r_s = −0.976: strong negative correlation: runners who train more tend to run 2 km faster.
2. (b) No. r_s is not exactly −1, so the ranks are not perfectly reversed: at least one runner trains more than another but is slower. 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.