12. Computing power
Suppose an architectural firm specializing in the structural restoration and renovation of historic homes and early barns is deciding whether to open a branch of the company in Wilmington, Vermont. Market research commissioned by the firm indicates that the Vermont location will be profitable only if the mean age of houses and barns located within a 100-mile radius of Wilmington is greater than 65 years.
The architectural firm conducts a hypothesis test to determine whether μ, the mean age of structures located within a 100-mile radius of Wilmington, is greater than 65 years. The test is conducted at α = 0.05 level of significance using a random sample of n = 144 houses and barns located in the specified area. The population standard deviation of the age of structures is assumed to be known with a value of σ = 16.8 years. The firm will open a Vermont branch only if it rejects the null hypothesis that the mean age of structures in the specified area is less than or equal to 65 years.
To summarize this hypothesis test refer to the chart given below.