(a) Eight randomly sampled cereal boxes have masses 261, 249, 259, 252, 255, 256, 258, 254 grams. Find unbiased estimates of the population mean and variance. [3]

The supplier claims a mean mass of 253 g. A quality control officer suspects a greater mean. A new random sample of 100 boxes has total mass 25360 g.

(b)(i) Given a population standard deviation of 3.5 g, test at the 5% significance level whether the population mean exceeds 253 g. [5]

(b)(ii) An employee says the test is invalid because it uses the normal distribution when box masses are not known to be normal. Explain briefly whether this is true. [1]