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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.