B. Calculating the probability of a Type II error Suppose an architectural rm 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 rm indicates that the Vermont location will be protable only if the mean age of houses and barns located within a IUDmile radius of lWilmington is greater than 65 years. The architectural firm conducts a hypothesis test to determine whether p, the mean age of structures located within a IOUmile radius of ln'tl'ilmingtonr is greater than 65 years. The test is conducted at o = 0.01 leyel of significance using a random sample ofn = 195 houses and barns located in the specied area. The population standard deyiation of the age of structures is assumed to be known with a value of o = 23.8 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 55 years. The null hypothesis is rejected when the sample mean 1: is V . Therefore, the architectural rm will make the decision not to open a branch in Vermont ifi is Y (Hint: Use the tool to obtain the sampling distribution of 5C) Suppose that the true value of u is 69 years. The probability:l that the architecture firm commits a Type II error is V . If the true value of p is 69 yearsJ the power of the test is V