An industrial chemist is investigating the relationship between the reaction temperature, T T\,T in Kelvin (K\text{K}K), and the resulting chemical yield, Y Y\,Y in grams (g\text{g}g), of a specific synthetic process. A series of 12 experimental trials is conducted, and the data are recorded.
The summary statistics for the trials are as follows:
n=12,∑T=3900,∑Y=1800,∑Y2=273600,STT=2400,STY=2100 n = 12, \quad \sum T = 3900, \quad \sum Y = 1800, \quad \sum Y^2 = 273600, \quad S_{TT} = 2400, \quad S_{TY} = 2100 n=12,∑T=3900,∑Y=1800,∑Y2=273600,STT=2400,STY=2100Calculate the product moment correlation coefficient between T T\,T and YYY.
Give an interpretation of your product moment correlation coefficient in the context of the study.
Find the equation of the least squares regression line of Y Y\,Y on T T\,T in the form Y=a+bTY = a + bTY=a+bT.
Give an interpretation of the value of b b\,b in your regression line.
(i) Use the regression line from part (c) to estimate the chemical yield for a reaction performed at a temperature of 380 K.
(ii) Comment on the reliability of your answer in part (i) given that the range of temperatures in the sample was 305 K to 345 K.
Using the regression line from part (c), the researcher estimates that for a temperature increase of x Kx\text{ K}x K, there will be an increase of 14 g in the chemical yield.
Find the value of xxx.
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.