Question

A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 21 houses that sold in their neighborhood took an average time of 120 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 25 days.

a. What assumption regarding the population is necessary for making an interval estimate for the population mean? Assume that the central limit theorem applies. Assume that the population has a normal distribution.

b. Construct the 99% confidence interval for the mean sale time for all homes in the neighborhood.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 120

Population standard deviation =    = 25

Sample size = n = 21

a) Assume that the population has a normal distribution

b) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_{0.005 =} 2.576

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

= 2.576 * ( 25 /  21)

= 14.05

At 99% confidence interval estimate of the population mean is,

  ± E

120 ± 14.05   

( 105.95, 134.05 )