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.
Assuming a confidence level of 95%, determine the margin of error in estimating the average cost of accessories on Mini Coopers

Answer 1

Solution :

Given that,

sample standard deviation = s = 1500

sample size = n = 179

Degrees of freedom = df = n - 1 = 178

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,178 = 2.604

Margin of error = E = t_/2,df * (s /n)

= 2.604 * (1500 / 179)

= 34.839

The margin of error in estimating the average cost of accessories on Mini Coopers is 34.839.