4. A town council is concerned that the mean price of renting two bedroom flats in the town has exceeded \(\pounds 650\) per month. A random sample of eight two bedroom flats gave the following results, \(\pounds x\), per month. $$705 , \quad 640 , \quad 560 , \quad 680 , \quad 800 , \quad 620 , \quad 580 , \quad 760$$ [You may assume \(\sum x = 5345 \quad \sum x ^ { 2 } = 3621025\) ]

1. Find a 90\% confidence interval for the mean price of renting a two bedroom flat.
2. State an assumption that is required for the validity of your interval in part (a).
3. Comment on whether or not the town council is justified in being concerned. Give a reason for your answer.