The carbon mass percentage, CCC, and the Vickers hardness index, HHH, of n=12n = 12n=12 steel alloy specimens were recorded during a quality control test.
Summary statistics for the data are as follows:
∑C=5.4∑C2=2.5074SHH=45.6SCH=1.62 \sum C = 5.4 \quad \sum C^2 = 2.5074 \quad S_{HH} = 45.6 \quad S_{CH} = 1.62 ∑C=5.4∑C2=2.5074SHH=45.6SCH=1.62(i) Calculate the mean carbon mass percentage, Cˉ\bar{C}Cˉ.
(ii) Show that the standard deviation of the carbon mass percentages is 0.08030.08030.0803 to 3 significant figures.
Calculate the product moment correlation coefficient (PMCC) between CCC and HHH.
For an industrial report, the carbon data were transformed using the linear coding P=100C−10P = 100C - 10P=100C−10.
Use your results from part (a) to calculate the mean and the standard deviation of the transformed values, PPP.
Given that QQQ is the transformed hardness index using the same linear coding Q=100H−10Q = 100H - 10Q=100H−10, state the value of the product moment correlation coefficient between PPP and QQQ. Give a reason for your answer.
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.