5.07a Non-parametric tests: when to use

A motoring organisation wishes to determine whether or not the petrol consumption of two different car models A and B are the same. A trial is therefore carried out in which 6 cars of each model are given 10 litres of petrol and driven at a predetermined speed around a track until the petrol is used up. The distances travelled, in miles, are shown below Model A: \(86.3 \quad 84.2 \quad 85.8 \quad 83.1 \quad 84.7 \quad 85.3\) Model B: \(84.9 \quad 85.9 \quad 84.8 \quad 86.5 \quad 85.2 \quad 85.5\) It is proposed to use a test with significance level 5% based on the Mann-Whitney statistic \(U\).

1. State suitable hypotheses. [2]
2. Find the critical region for the test. [3]
3. Determine the value of \(U\) for the above data and state your conclusion in context. You must justify your answer. [4]

A medical student is investigating two different methods, A and B, of measuring a patient's blood pressure. He believes that Method B gives, on average, a higher reading than Method A so he defines the following hypotheses. \(H_0\): There is on average no difference in the readings obtained using Methods A and B; \(H_1\): The reading obtained using Method B is on average higher than the reading obtained using Method A. He selects 10 patients at random and he measures their blood pressures using both methods. He obtains the following results.

1. Carry out an appropriate Wilcoxon signed rank test on this data set, using a 5% significance level. [6]
2. State what conclusion the medical student should reach, justifying your answer. [2]