Suppose that in past years the average price per square foot for warehouses in the United States has been $31.28. A national real estate investor wants to determine whether that figure has changed now. The investor hires a researcher who randomly samples 50 warehouses that are for sale across the United States and finds that the mean price per square foot is $30.64, with a standard deviation of $1.22. Assume that prices of warehouse footage are normally distributed in population. If the researcher uses a 5% level of significance, what statistical conclusion can be reached?
Solution :
The null and alternative hypothesis is ,
H0 :
= 31.28
Ha :
31.28
Test statistic (t) =
= (
-
) / s /
n
= (30.64 - 31.28) / 1.22 /
50
Test statistic = -3.71
P-value = 0.0005
= 0.05
P-value <
Reject the null hypothesis .
There is sufficient evidence to support the claim.
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