A chemical plant measures the mass of a reactant, xxx (in units of 10 kg), and the resulting yield of a purified catalyst, yyy (in decigrams), for a random sample of 12 batches. The data are summarised as follows:
∑x=360∑x2=12000∑y=144∑y2=1928 \sum x = 360 \quad \sum x^2 = 12000 \quad \sum y = 144 \quad \sum y^2 = 1928 ∑x=360∑x2=12000∑y=144∑y2=1928and the regression line of yyy on xxx has equation y=1.5+0.35xy = 1.5 + 0.35xy=1.5+0.35x.
Use the regression line to estimate the yield in grams for a batch using 470 kg of reactant.
Find SyyS_{yy}Syy and SxxS_{xx}Sxx.
Calculate the product moment correlation coefficient between yyy and xxx.
An 13th batch is added to the sample. It involves 300 kg of reactant and a yield of 1.525 grams of catalyst.
Use the formula Sxy=∑(x−xˉ)(y−yˉ)S_{xy} = \sum (x - \bar{x})(y - \bar{y})Sxy=∑(x−xˉ)(y−yˉ) to show that the value of SxyS_{xy}Sxy for the 13 batches will be the same as it was for the original 12 batches.
Find the new equation of the regression line of yyy on xxx for the 13 batches.
Comment on the suitability of using the new regression line to estimate the yield for a batch using 1800 kg of reactant. Provide 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.