A climatologist is investigating the relationship between the altitude, hhh km, at which a sensor is placed and the intensity of cosmic rays, ccc counts per minute (cpm), detected. The climatologist collects data from 8 distinct high-altitude balloons. The results are recorded in the table below.
| Altitude hhh (km) | 1.1 | 2.4 | 3.5 | 4.2 | 5.8 | 6.5 | 8.1 | 10.3 |
|---|---|---|---|---|---|---|---|---|
| Intensity ccc (cpm) | 210 | 340 | 420 | 510 | 800 | 760 | 1200 | 1550 |
Calculate Spearman's rank correlation coefficient for these data.
The climatologist believes that there is a positive correlation between altitude and cosmic ray intensity. Stating your hypotheses clearly, test this belief at the 5% level of significance.
State the required condition for a product moment correlation coefficient (PMCC) to be a valid test of association between these two variables.
For this sample, the mean intensity is 723.75 cpm and the median intensity is 635 cpm. Explain whether these statistics suggest that the condition stated in part (c) is likely to be met.
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.