(b) (i) (i) (ii) A random sample of size n is drawn from a normal population with mean u and variance 02. State, as illy as you can, the distribution of the sample mean. (2 marks) Explain the different circumstances in which a onetailed or a two-tailed test of signicance of a sample means should be used. (2 marks) A paint manufacturer claims that the mean amount of colour in an oil- based paint is 7.0g per kilogram of paint. Tests on a random sample of 8 one-kilogram tins yielded the following amounts of colour, in grams. 6.8 6.9 7.2 7.1 7.3 7.3 7.7 7.4 Assuming that the amount of colour in a one-kilo gram tin of paint has a normal distribution, perform a test, at the 5% signicance level, to determine whether these data supply evidence that the mean amount of colour in a one-kilogram tin of paint is greater than 7.0g. (12 marks) (Total: 20 marks)