An environmental agency monitors air quality at 8 different urban locations using two different portable sensors, Alpha (AAA) and Beta (BBB). The particulate matter readings (μg/m3\mu g/m^3μg/m3) recorded at the same time are shown in the table below:
| Location | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 |
|---|---|---|---|---|---|---|---|---|
| Sensor Alpha (AAA) | 45 | 32 | 58 | 21 | 15 | 60 | 10 | 25 |
| Sensor Beta (BBB) | 40 | 35 | 50 | 28 | 12 | 65 | 18 | 22 |
Calculate Spearman's rank correlation coefficient for these data.
Test, at the 5% level of significance, whether there is a positive correlation between the readings of the two sensors. State your hypotheses clearly.
Sensor Beta was later found to have a calibration error at Location L2; the reading should have been 40 instead of 35.
Without performing any further calculations, explain the procedure for finding Spearman’s rank correlation coefficient given this change.
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.