An apparatus for determining g, the acceleration due to gravity, has standard deviation , when used at one place and , at another. It is proposed to make N determinations-some at one place, some at the other-to find the difference between g at the two places. Determine the optimum allocation of the determinations between the two places in order to minimize the posterior variance of the difference. If = 0.0625, = 0-1250 find how large the observed mean difference will have to be before a test of the hypothesis that the real difference is zero is significant at the 5% level. How large must N be if the real difference is 0-25 and we wish to have a 90% chance of the above test yielding a significant result?