The average price of homes sold in the U.S. in 2012 was $240,000. A sample of 144 homes sold in Chattanooga in 2012 showed an average price of $246,000. It is known that the standard deviation of the population () is $36,000. We are interested in determining whether or not the average price of homes sold in Chattanooga is significantly more than the national average.Compute the test statistic.
Question
The average price of homes sold in the U.S. in 2012 was 246,000. It is known that the standard deviation of the population () is $36,000. We are interested in determining whether or not the average price of homes sold in Chattanooga is significantly more than the national average.Compute the test statistic.
Solution
To compute the test statistic, we will use the formula for a z-score, which is:
Z = (X - μ) / (σ / √n)
where:
- X is the sample mean
- μ is the population mean
- σ is the standard deviation of the population
- n is the sample size
In this case:
- X = $246,000 (the average price of homes sold in Chattanooga)
- μ = $240,000 (the average price of homes sold in the U.S.)
- σ = $36,000 (the standard deviation of the population)
- n = 144 (the number of homes sold in Chattanooga)
Substituting these values into the formula, we get:
Z = (240,000) / (6,000 / (6,000 / $3,000 = 2
So, the test statistic (Z) is 2. This means that the average price of homes sold in Chattanooga is 2 standard deviations above the national average.
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