A family is relocating from St. Louis, Missouri, to California. Due to an increa

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 26 houses that sold in their neighborhood took an average time of 75 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 8 days. Use Table 1.

What assumption regarding the population is necessary for making an interval estimate for the population mean?

Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places and final answer to 2 decimal places.)

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 26 houses that sold in their neighborhood took an average time of 75 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 8 days. Use Table 1.

Explanation / Answer

Assume that the population has a normal distribution.

Given a=0.1, |Z(0.05)|=1.645 (from standard normal table)
So 90% confidence interval is
xbar +/- Z*s/vn
--> 75+/- 1.645* 8/sqrt(26)
--> (194.772, 241.228)

75-2.5808 ,75 +2.5808

72.4191,77.5808

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