An engineering firm is testing a new solar panel design. They investigated the relationship between the energy conversion efficiency, EEE (%), and the average operating temperature, TTT (°C), for a sample of 8 test units. They also recorded a subjective durability rating, RRR, for each unit, where 1 indicates the most durable and 8 indicates the least durable.
| Unit | Efficiency EEE (%) | Durability Rating RRR |
|---|---|---|
| U1U_1U1 | 21.4 | 7 |
| U2U_2U2 | 26.8 | 2 |
| U3U_3U3 | 24.3 | 5 |
| U4U_4U4 | 27.9 | 1 |
| U5U_5U5 | 25.1 | 4 |
| U6U_6U6 | 21.1 | 8 |
| U7U_7U7 | 27.2 | 3 |
| U8U_8U8 | 22.9 | 6 |
The following summary statistics were calculated for temperature and efficiency:
STT=244.5,SEE=48.2,STE=−92.4 S_{TT} = 244.5, \quad S_{EE} = 48.2, \quad S_{TE} = -92.4 STT=244.5,SEE=48.2,STE=−92.4Calculate the product moment correlation coefficient (PMCC) between energy conversion efficiency and operating temperature.
Use your value from part (a) to test, at the 1% significance level, whether there is evidence of a negative correlation between efficiency and temperature. State your hypotheses clearly.
State a required assumption regarding the variables for the test in part (b) to be valid.
Calculate the Spearman's rank correlation coefficient between efficiency and durability rating.
Using a 5% level of significance and a two-tailed test, determine whether there is evidence of a correlation between efficiency and durability rating.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.