For fixed s, the random variable has expectations and variance , the same for all s. The random variables has expectation and variance . Find the unconditional expectation and variance of r. For each of several rock samples from a small region the strength of the remanant magnetism is determined in the laboratory. The laboratory error in determining the magnetism of a sample is known to be free from bias and have variance = 0.36. There may, however, be variations between samples of unknown variance . For the determinations for 10 samples given below carry out a significance test to see if there is evidence for suspecting this second source of variation, and if so give limits between which most probably lies. 11-80, 9-23, 11-73, 11-78, 10-21, 9-65, 10-62, 9-76, 8-81, 9.66. (The sum of the values is 103-25, the sum of the squares about the mean is 11-07825; the units are conventional.) (Camb. N.S.)