A sound engineer conducts an experiment to investigate the relationship between the peak volume levels of a concert PA system and the perceived audio clarity for the audience. At five different locations, A,B,C,D A, B, C, D\,A,B,C,D and EEE, the peak volume vvv (in decibels) and a clarity score sss (on a scale from 0 to 100) are recorded. The results are summarized in the table below:
| Location | AAA | BBB | CCC | DDD | EEE |
|---|---|---|---|---|---|
| Volume vvv (dB) | 98 | 105 | 92 | 112 | 100 |
| Clarity sss (score) | 62 | 48 | 85 | 35 | 70 |
Determine the value of Spearman’s rank correlation coefficient for these data.
The engineer suspects that higher volume levels lead to a decrease in perceived clarity. Test this suspicion at the 5% level of significance, stating your hypotheses clearly.
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.