A study was made to determine the amount of fuel economy obtained by using a specific new type of tyre over a standard type. For this reason, 8 cars were fitted with the new type of tyre and the fuel consumption (in km/l) was measured after a test drive. Afterwards, the same cars with the same drivers were fitted with the standard type of tyre and the experiment was repeated to obtain the following fuel consumption measurements.

Car #1 #2 #3 #4 #5 #6 #7 #8

New type tyres 4.6 6.5 7.4 5.5 5.3 5.2 6.6 6.7

Standard type tyres 4.1 6.2 7.1 5.4 5.5 5.1 6.1 6.3

(a) Carry out an appropriate hypothesis test to determine whether the fuel consumption is different between the two types of tyre. State the test hypotheses, and specify your test statistic and its distribution under the null hypothesis. Comment on your findings.

(b) State any assumptions you made in (a).

(c) Give a 95% confidence interval for the difference in means.

(d) On the basis of the data alone, would you be concerned about fuel consumption if you wanted to buy the new type of tyre? Provide an explanation with your answer.