b) Fifty bars of soap are manufactured in each of two ways. Two charac- teristics, x1 =lather and $2 =mildness, are measured. The summary statistics for bars produced by methods 1 and 2 are, respectively: * (1 ) 8.3 2 = 4.1 S1 = 1 6 * (2) = 10.2 3.9 $ 2 = (? 4 Test the hypothesis Ho : u(!) = u(2) against H1 : u(1) # u(2). State necessary assumptions for the test to be valid. [10