Question

The owner of a new car dealership claims the average number of days it takes his dealership to sell a Chevrolet Aveo is 50 days. A random sample of 50 cars had a mean time on the dealer’s lot of 64 days. Assume the population standard deviation to be 7.0 days. Find the 95% confidence interval estimate of the population mean. State the Margin of Error, Best Point Estimate and Include the written statement

Please list all the work.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 64

Population standard deviation =    = 7.0

Sample size n =50

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* ( 7.0/ 50 )

= 1.9403
At 95% confidence interval estimate of the population mean
is,

- E < < + E

64 - 1.9403 <   < 64 + 1.9403

62.0597 <   < 65.9403

( 62.0597 , 65.9403 )

Point estimate = sample mean =     = 64