Spearman's rank correlation Problem set A

A theatre records the ticket price and the attendance at eight shows. Calculate Spearman's rank correlation coefficient.

Eight students record the number of books read in a term and their score on a reading test. Calculate Spearman's rank correlation coefficient.

Two judges place eight dancers, A to H, in order, from 1st place to 8th place.

1. (a) Write down the rank each judge gave to A, B, C, D, E, F, G and H, in that order.
2. (b) Calculate Spearman's rank correlation coefficient.

A shop records its weekly advertising spend (hundreds of pounds) and its sales (units) over seven weeks. Use Spearman's rank correlation to test, at the 5% significance level, whether there is a positive correlation. The critical value is 0.714.

1. (a) State the hypotheses.
2. (b) Calculate r_s.
3. (c) State the conclusion in context.

Eight students record their weekly hours of television (x) and their test mark (y). Use Spearman's rank correlation to test, at the 10% significance level, whether there is a negative correlation. The critical value is 0.524.

1. (a) State the hypotheses.
2. (b) Calculate r_s.
3. (c) State the conclusion in context.

A park keeper records the age of nine trees (years) and their height (metres). The critical value for a two-tailed test at the 5% significance level is 0.700.

1. (a) Calculate r_s.
2. (b) Test, at the 5% significance level, whether there is any correlation. State the hypotheses and the conclusion in context.

Two judges score six singers out of 10.

1. (a) Calculate r_s.
2. (b) The critical value for a one-tailed test at the 5% significance level is 0.829. Determine whether there is significant evidence that the two judges tend to agree.

Eight runners record their weekly training distance (km) and their time for a 2 km run (minutes).

1. (a) Calculate r_s and describe the correlation in context.
2. (b) A coach says that runners who train more always run faster. Does the data support this claim?

The scatter diagram shows the height y (mm) of a plant at week x for ten plants. For these data Pearson's r = 0.692 and Spearman's r_s = 0.964. The point (10, 230) was misrecorded. The correct value is (10, 62).

1. (a) Without calculating, say how the new value of Pearson's r compares with the old value.
2. (b) Without calculating, say how the new value of r_s compares with the old value.
3. (c) The heights are converted from millimetres to centimetres. How does this affect r_s?

A culture of bacteria is counted each hour. The number of bacteria is shown.

1. (a) Calculate r_s.
2. (b) Pearson's r for these data is 0.850. Explain why r_s = 1 although r is less than 1.