3 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, \(x \mathrm {~km}\), that he flew in 50 randomly chosen weeks and summarised the results as follows. $$n = 50 \quad \Sigma x = 143300 \quad \Sigma x ^ { 2 } = 410900000$$

1. Calculate unbiased estimates of the population mean and variance.
2. 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.