A3 a) b} In Britain the average car insurance premium is 450 per annum. Would you expect it to be cheaper in rural Wales? To test that a sample of twenty-five motorists in south Gwynedd, were asked how much they pay for insurance in 2020. The mean cost of 440 and a standard deviation of 45. Construct a hypothesis test and report on your findings. Use a significance value of 0.05. 10 marks The Office of National statistics report that the average duration of unemployment for working age adults was twenty weeks in the North of England, with a population standard deviation of five weeks. This com pa red to a duration of sixteen weeks, with a population standard deviation of six weeks in the South of England. Assume a sample size of one hundred in both regions. What is the probability ofa sample of one hundred having a mean within one week of the population mean for: 1) the North of England, and 2] the South of England? Comment on your findings 10 marks