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A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Houston. His main concern is the total market value of the 3,605 houses in the suburban county. He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700. The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400. Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
If he wants a 95% confidence on estimating the true population mean market price of the houses in the suburban county to be within $10,000, how large a sample will he need?
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