3 Judith believes that mathematical ability and chess-playing ability are related. She asks 20 randomly chosen chess players, with known British Chess Federation (BCF) ratings X, to take a mathematics aptitude test, with scores Y. The results are summarised as follows. n = 20, Ex = 3600, Ex- = 660500, Ey = 1440, Ey? = 105280, Exy = 260990 (a) Calculate the value of Pearson's product-moment correlation coefficient r. [2] (b) State an assumption needed to be able to carry out a significance test on the value of r. [1] (c) Assume now that the assumption in part (ii) is valid. Test at the 5% significance level whether there is evidence that chess players with higher BCF ratings are better at mathematics. [4] (d) There are two different grading systems for chess players, the BCF system and the international ELO system. The two sets of ratings are related by ELO rating = 8 x BCF rating + 650. Magnus says that the experiment should have used ELO ratings instead of BCF ratings. Comment on Magnus's suggestion. [1] (a) Calculate the value of Pearson's product-moment correlation coefficient r. [2] (b) State an assumption needed to be able to carry out a significance test on the value of r. [1] (c) Assume now that the assumption in part (b) is valid. Test at the 5% significance level whether there is evidence that chess players with higher BCF ratings are better at mathematics. [4] (d) There are two different grading systems for chess players, the BCF system and the international ELO system. The two sets of ratings are related by ELO rating = 8 # BCF rating + 650. Magnus says that the experiment should have used ELO ratings instead of BCF ratings. Comment on Magnus's suggestion. [1]