Question: a company offers the service of doing the paperwork associated...

A company offers the service of doing the paperwork associated with claiming tax back for workers. They claim in an advertising campaign that the average amount their clients receive is £450. A survey of 150 randomly selected clients of the company recorded the amount that each received and the average was £383 with a standard deviation of £93.

i. Construct a 99% confidence interval.

ii. Interpret the interval and discuss the validity of the claim made by the company.

iii. A graph of the raw data indicated that the data came from a population with a distribution that was skewed to the right. What effect does this have on the validity of the confidence interval and its interpretation?