In an aerospace engineering trial, 7 experimental prototype wings were tested in a wind tunnel to determine the relationship between atmospheric pressure, ppp (kPa), and the resulting lift coefficient, LLL. The data collected is presented in the table below:
| Prototype Unit | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| Pressure, ppp | 45 | 52 | 60 | 68 | 75 | 83 | 91 |
| Lift, LLL | 0.42 | 0.48 | 0.46 | 0.55 | 0.51 | 0.62 | 0.58 |
Calculate the value of Spearman's rank correlation coefficient between ppp and LLL.
Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence of a positive correlation between atmospheric pressure and lift coefficient.
The product moment correlation coefficient (PMCC) for these data is calculated as r=0.8881r = 0.8881r=0.8881.
Use the given PMCC value to test, at the 5% level of significance, whether there is evidence of a positive correlation between pressure and lift.
Based on your conclusions from parts (b) and (c), describe the nature of the relationship between atmospheric pressure and lift coefficient.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.