6 A company has a large fleet of cars. It is claimed that use of a fuel additive will reduce fuel consumption. In order to test this claim a researcher at the company randomly selects 40 of the cars. The fuel consumption of each of the cars is measured, both with and without the fuel additive. The researcher then calculates the difference \(d\) litres per kilometre between the two figures for each car, where \(d\) is the fuel consumption without the additive minus the fuel consumption with the additive. The sample mean of \(d\) is 0.29 and the sample standard deviation is 1.64 .

1. Showing your working, find a 95\% confidence interval for the population mean difference.
2. Explain whether the confidence interval suggests that, on average, the fuel additive does reduce fuel consumption.
3. Explain why you can construct the interval in part (i) despite not having any information about the distribution of the population of differences.
4. Explain why the sample used was random.