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​ 95% confidence interval for the average cost of accessories on Mini Coopers.

Answer 1

Answer:
`(24980.25,\ 25419.75)`

Explanation:

The confidence interval for population mean is given by :-

`\overline{x}\pm z_(\alpha/2)(\sigma)/(√(n))`

Given : Sample size :
`n= 179` , which is a large sample , so we apply z-test .

Sample mean :
`\overline{x}=20200+5000=25200`

Standard deviation :
`\sigma= 1500`

Significance level :
`\alpha=1-0.95=0.05`

Critical value :
`z_(\alpha/2)=1.96`

Now, a confidence interval at the 95% level of confidence will be :-

`25200\pm(1.96)(1500)/(√(179))\\\\\approx25200\pm219.75\\\\=(25200-219.75,\ 25200+219.75)\\\\=(24980.25,\ 25419.75)`