Question 1 - A-Level Maths

Exam Board	Edexcel
Module	S3 (Statistics 3)
Year	2014
Session	June
Topic	Hypothesis test of Spearman’s rank correlation coefficien

A journalist is investigating factors which influence people when they buy a new car. One possible factor is fuel efficiency. The journalist randomly selects 8 car models. Each model's annual sales and fuel efficiency, in km/litre, are shown in the table below.

Calculate Spearman's rank correlation coefficient for these data. The journalist believes that car models with higher fuel efficiency will achieve higher sales.
Stating your hypotheses clearly, test whether or not the data support the journalist's belief. Use a \(5 \%\) level of significance.
State the assumption necessary for a product moment correlation coefficient to be valid in this case.
The mean and median fuel efficiencies of the car models in the random sample are 14.5 km /litre and 15.65 km /litre respectively. Considering these statistics, as well as the distribution of the fuel efficiency data, state whether or not the data suggest that the assumption in part (c) might be true in this case. Give a reason for your answer. (No further calculations are required.)