Legend has it that Archimedes made his discovery concerning specific gravity (Archimedes' principle) while trying to determine whether the king's crown was made of pure gold or an alloy. Working with metal samples which he knew to be pure gold or alloys, he found that his device for measuring specific gravity produced a mean determination of µ = 19.3 for pure gold, whereas all alloys tested yielded lower mean specific gravities. For the sake of this problem, suppose Archimedes' measuring device followed an N(m, 0.09) distribution.
a. What would be a suitable null hypothesis for such an experiment?
b. What would be the most logical alternative hypothesis?
c. If a = 0.05, what should be the region of rejection for this experiment?
d. How likely is it that a random sample of an alloy with a specific gravity determination of 18.7 would be mistakenly called pure gold in this experiment?