Specimens of milk from a number of dairies in three different districts were analyzed, and the concentration of the radioactive isotope strontium-90 was measured in each specimen. Suppose that specimens were obtained from four dairies in the first district, from six dairies in the second district, and from three dairies in the third district, and that the results measured in picocuries per liter were as follows:
District 1: 6.4, 5.8, 6.5, 7.7,
District 2: 7.1, 9.9, 11.2, 10.5, 6.5, 8.8,
District 3: 9.5, 9.0, 12.1.
a. Assuming that the variance of the concentration of strontium-90 is the same for the dairies in all three districts, determine the M.L.E. of the mean concentration in each of the districts and the M.L.E. of the common variance.
b. Test the hypothesis that the three districts have identical concentrations of strontium-90.