Product moment and Spearman's rank correlationEdexcel A-Level Further Maths: Mind map

Exam questions on Product moment and Spearman's rank correlation

1. A researcher records the hours of sleep, $x$, and the reaction time, $y$ ms, of each of 8 randomly chosen students. The summary statistics are $S_{xx}=62.5$, $S_{yy}=40$ and $S_{xy}=-45$.
   Interpret the value of $r$ between $x$ and $y$ in context, and state an assumption about the population needed to use $r$ in a hypothesis test.2 marks
2. Two judges each rank six paintings, $A$ to $F$, from 1 (best) to 6 (worst). Judge 1 ranks $A$ to $F$ as $3, 1, 2, 5, 4, 6$ respectively. Judge 2 ranks them as $2, 1, 4, 5, 3, 6$ respectively.
   State, with a reason, whether Spearman's rank correlation coefficient or the product moment correlation coefficient is more appropriate for these data.2 marks
3. Seven students sit a mathematics test and a physics test. Their scores, in the order of students $1$ to $7$, are: mathematics $56, 61, 61, 70, 48, 75, 66$ and physics $50, 58, 49, 64, 44, 70, 60$.
   Rank the mathematics scores and the physics scores from lowest (rank 1) to highest, and hence show that $\sum d^2=3.5$.3 marks