The temperature of heat treatment, TTT in ∘C^\circ\text{C}∘C, and the resulting tensile strength, SSS in MPa, of a random sample of 8 experimental alloy specimens are shown in the table below.
| Specimen | P | Q | R | S | T | U | V | W |
|---|---|---|---|---|---|---|---|---|
| Temperature (TTT) | 200 | 250 | 300 | 350 | 400 | 450 | 500 | 550 |
| Strength (SSS) | 420 | 410 | 460 | 450 | 490 | 480 | 530 | 510 |
Given that STT=105 000S_{TT} = 105\,000STT=105000, SSS=12 287.5S_{SS} = 12\,287.5SSS=12287.5 and STS=33 250S_{TS} = 33\,250STS=33250, calculate, to 3 decimal places, the product moment correlation coefficient (PMCC) between heat treatment temperature and tensile strength.
Using a 5% significance level, test whether there is evidence of a positive correlation between treatment temperature and tensile strength. State your hypotheses clearly.
An apprentice, Jonas, inspects the 8 specimens and ranks them by 'expected durability' based on surface finish. His ranking from least durable to most durable is:
Q,R,P,T,S,V,W,U Q, R, P, T, S, V, W, U Q,R,P,T,S,V,W,UFind, to 3 decimal places, Spearman's rank correlation coefficient between Jonas's durability ranks and the actual tensile strength rankings.
Use your value from part (c) to test whether Jonas has a significant ability to rank the specimens by strength at a 5% significance level. State your hypotheses clearly.
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.