The following coded pairs of measurements were taken of the temperature (X) and thrust (I) of...

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The following coded pairs of measurements were taken of the temperature (X) and thrust (I) of a jet engine while it was being tested under uniform operating conditions. X y 33 15 20 26 30 25 1.4 1.2 1.9 1.6 2.5 2.1 34 35 38 39 41 46 49 52 57 2.4 1.5 2.3 2.7 1.8 2.2 2.8 3.4 3.2 You are given that x=540, x=21412, y = 33.0, =78.54, xy = 1276.6. (i) (a) (b) Plot the data on a scatter diagram and comment on the suitability of the Pearson product-moment correlation coefficient, r, as a measure of the association between thrust and temperature. (6) Calculate r for these data, and test at the 5% significance level the hypothesis of zero correlation against the alternative that thrust and temperature are positively correlated. State clearly (but do not prove) any formulae that you have used, and list the assumptions you have made in the test. (6) (ii) A colleague wishes to test at the 5% significance level the hypothesis of no trend against the alternative of an increasing trend, without assuming that the trend is necessarily linear. State what measure of association he should use, calculate it for the above data and carry out the desired test. Compare the result of this test with your findings in part (i). (8) The following coded pairs of measurements were taken of the temperature (X) and thrust (I) of a jet engine while it was being tested under uniform operating conditions. X y 33 15 20 26 30 25 1.4 1.2 1.9 1.6 2.5 2.1 34 35 38 39 41 46 49 52 57 2.4 1.5 2.3 2.7 1.8 2.2 2.8 3.4 3.2 You are given that x=540, x=21412, y = 33.0, =78.54, xy = 1276.6. (i) (a) (b) Plot the data on a scatter diagram and comment on the suitability of the Pearson product-moment correlation coefficient, r, as a measure of the association between thrust and temperature. (6) Calculate r for these data, and test at the 5% significance level the hypothesis of zero correlation against the alternative that thrust and temperature are positively correlated. State clearly (but do not prove) any formulae that you have used, and list the assumptions you have made in the test. (6) (ii) A colleague wishes to test at the 5% significance level the hypothesis of no trend against the alternative of an increasing trend, without assuming that the trend is necessarily linear. State what measure of association he should use, calculate it for the above data and carry out the desired test. Compare the result of this test with your findings in part (i). (8)