Question

# A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of...

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 15 houses that sold in their neighborhood took an average time of 280 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 66 days. [You may find it useful to reference the z table.] a. What assumption regarding the population is necessary for making an interval estimate for the population mean? Assume that the population has a normal distribution. Assume that the central limit theorem applies. b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

Solution :

Given that,

Point estimate = sample mean = = 280

Population standard deviation =    = 66

Sample size = n = 15

a) Assumption regarding the population mean sale time for all homes in the neighborhood.

Assume that the population has a normal distribution because n 30

b) At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * ( 66 /  15 )

= 28.03

At 90% confidence interval estimate of the population mean is,

± E

280 ± 28.03

( 251.97, 308.03)

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