Spearman's rank correlation Problem set B

A student records the minutes of practice each day and the score in a weekly quiz, over eight weeks. Calculate Spearman's rank correlation coefficient.

Eight students record their minutes of daily revision and their mark in a short quiz. Calculate Spearman's rank correlation coefficient.

Two film critics place eight films, 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 kiosk records the weekly hours of sunshine and the number of ice creams sold (tens) 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 the number of days they were absent (x) and their exam 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 garage records the speed of nine test drives (km/h) and the fuel economy (miles per gallon). 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 coaches score six gymnasts 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 coaches tend to agree.

Eight adults record their weekly exercise (hours) and their systolic blood pressure (mmHg).

1. (a) Calculate r_s and describe the correlation in context.
2. (b) A newspaper says that people who exercise more always have lower blood pressure. Does the data support this claim?

The scatter diagram shows the mass y (kg) of a crop after x doses of fertiliser, for ten plots. For these data Pearson's r = 0.697 and Spearman's r_s = 0.964. The point (10, 160) was misrecorded. The correct value is (10, 45).

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 masses are converted from kilograms to grams. How does this affect r_s?

The side length x (cm) and the volume y (cm³) of eight cubes are shown.

1. (a) Calculate r_s.
2. (b) Pearson's r for these data is 0.932. Explain why r_s = 1 although r is less than 1.