The dosage of a new bio-stimulant, in ml, and the final yield, in grams, of a random sample of 8 experimental crop plots are shown in the table below.
| Plot | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Stimulant (xxx) | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 |
| Yield (yyy) | 42 | 58 | 53 | 71 | 65 | 84 | 81 | 95 |
Given that Sxx=1050S_{xx} = 1050Sxx=1050, Syy=2169.875S_{yy} = 2169.875Syy=2169.875 and Sxy=1432.5S_{xy} = 1432.5Sxy=1432.5, calculate, to 3 decimal places, the product moment correlation coefficient (PMCC) between stimulant dosage and yield for these plots.
Using a 5% significance level, test whether there is evidence of a positive correlation between stimulant dosage and crop yield. State your hypotheses clearly.
An agricultural student, Jamie, observes the 8 plots and ranks them by yield based on visual health alone. Jamie's ranking from lowest yield to highest yield is:
C,A,B,E,D,F,G,H C, A, B, E, D, F, G, H C,A,B,E,D,F,G,HFind, to 3 decimal places, Spearman's rank correlation coefficient between Jamie's ranks and the actual yield rankings.
Use your value from part (c) to test whether Jamie has a significant ability to rank the plots by yield at a 5% significance level. State your hypotheses clearly.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.