Question

According to USA Today, customers are not settling for automobiles straight off the production lines. As an example, those who purchase a $355,000 Rolls-Royce typically add $25,000 in accessories. One of the affordable automobiles to receive additions is BMW's Mini Cooper. A sample of 179 recent Mini purchasers yielded a sample mean of $5,000 above the $20,200 base sticker price. Suppose the cost of accessories purchased for all Mini Coopers has a standard deviation of $1,500.
Calculate a 99% confidence interval for the average cost of accessories on Mini Coopers

Answer 1

Given that, population standard deviation = $1500

sample size (n) = 179 and sample mean = $5000

A 99% confidence level has significance level of 0.01 and critical value is,

The 99% confidence interval for the population mean is,

Therefore, a 99% confidence interval for the average cost of accessories on Mini Coopers is ($4711.30, $5288.70).

Note : if we used critical value = 2.58 then required confidence interval is, ($4710.74, $5289.26)