A merchant figures her weekly profit to be a function of three variables: retail sales

Chapter 10, Problem 10.127

(choose chapter or problem)

A merchant figures her weekly profit to be a function of three variables: retail sales (denoted by X), wholesale sales (denoted by Y ), and overhead costs (denoted by W). The variables X, Y , and W are regarded as independent, normally distributed random variables with means 1, 2, and 3 and variances 2, a2, and b2, respectively, for known constants a and b but unknown 2. The merchants expected profit per week is 1 + 2 3. If the merchant has made independent observations of X, Y , and W for the past n weeks, construct a test of H0 :1 + 2 3 = k against the alternative Ha :1 + 2 3 = k, for a given constant k. You may specify = .05.