Suppose a Realtor is interested in comparing the asking prices of midrange homes

Question

Suppose a Realtor is interested in comparing the asking prices of midrange homes in Peoria, Illinois, and Evansville, Indiana. The Realtor conducts a small telephone survey in the two cities, asking the prices of midrange homes. A random sample of 21 listings in Peoria resulted in a sample average price of $116,900, with a standard deviation of $2,300. A random sample of 26 listings in Evansville resulted in a sample average price of $114,000, with a standard deviation of $1,750. The Realtor assumes prices of midrange homes are normally distributed and the variance in prices in the two cities is about the same.

What would he obtain for a 90% confidence interval for the difference in mean
prices of midrange homes between Peoria and Evansville?

Explanation / Answer

sample mean = 116900 +114000 /2 = 115450

sample std = sqrt(2300^2/21 + 1750^2/26) = 608.024032

upper limit = 115450 + 1.645 * 608.024 = 116450.20

lower limit = 115450 - 1.645 * 608.024 = 114449.80

hence confidence interval is

116450.20 < u < 114449.80

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