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:  $(24980.25,\ 25419.75)$

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

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 :-

$25200\pm(1.96)\dfrac{1500}{\sqrt{179}}\\\\\approx25200\pm219.75\\\\=(25200-219.75,\ 25200+219.75)\\\\=(24980.25,\ 25419.75)$