Following a change in flight schedules, an airline pilot wished to test whether the mean distance that he flies in a week has changed. He noted the distances, x km, that he flew in 50 randomly chosen weeks and summarised the results as follows. n = 50 Ex = 143 300 Ex- = 410900 000 (i) Calculate unbiased estimates of the population mean and variance. [3] (ii) In the past, the mean distance that he flew in a week was 2850 km. Test, at the 5% significance level, whether the mean distance has changed. [5]