(b) (i) (ii) A random sample of size n is drawn from a normal population with mean u and variance 0'2. State, as fully as you can. the distribution of the sample mean. {2 marks) Explain the different circumstances in which a one-tailed or a two-tailed test of significance of a sample means should be used. {2 marks) A paint manufacturer claims that the mean amount of colour in an oil- hased paint is 7.0g per kilogram of paint. Tissts 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-kilogram tin of paint has a normal distribution, perform a test, at the 5% significance level, to determine whether these data supply evidence that the mean amount of colour in a one-kilogram tin of paint is greater than 7.03. (12 marks) (Total: 2|] marks)