In: Statistics and Probability
According to a recent survey, a random sample of 100 homes sold in the Baton Rouge metro area had an average sale price of $263,000. If the population standard deviation of home prices is $20,000, what is the 99% confidence interval of the true population average sales price for homes sold in Baton Rouge?
Solution :
Given that,
Point estimate = sample mean =
= $263000
Population standard deviation =
= $20000
Sample size = n =100
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576 ( Using z table )
Margin of error = E = Z/2* ( /n)
=2.576 * ( 20000/ 100)
= 5152
At 99% confidence interval estimate of the population mean is,
- E < < + E
263000- 5152< <263000+ 5152
257848< < 268152
(257848, 268152)