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 20 houses that sold in their neighborhood took an average time of 130 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 30 days.

Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood

Answer 1

Since population standard deviation is known we use z-distribution       
90% confidence interval for population mean       
Given       
X̅ = 130          Sample Mean     
σ = 30          Population Standard Deviation     
n = 20             Sample Size     
Confidence interval for mean is given by       
          
For 90%, α = 0.10, α/2 = 0.05       
From the z-tables, or Excel function NORM.S.INV(α/2)       
z = NORM.S.INV(0.05) = 1.645   (We take the positive value for calculations)    

= (118.966, 141.034)       
       
90% confidence interval for the mean sale time for all homes in the neighborhood is (118.966, 141.034) days