Testing patient blood samples for HIV antibodies, a spectrophotometer determines the optical density of each sample. Optical density is measured as the absorbance of light at a particular wavelength. The blood sample is positive if it exceeds a certain cutofr value that is determined by the control samples for that run. Researchers are interested in comparing the laboratory variability for the positive control values. The data represent positive control values for 10 different runs at 4 randomly selected laboratories.(a) Write an appropriate model for this experiment.(b) Estimate the laboratory variance component and the variance withinlaboratories.

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Laboratory 2 3 1.325 Run 0.888 1.065 0.983 1.047 1.232 1.226 1.069 1.127 1.051 1.332 1.219 1.087 0.958 0.958 0.897 1.125 0.816 0.819 1.222 1.125 1.222 0.990 5 0.997 1.015 1.140 1.025 1.071 Laboratory 4. Run 0.969 0.905 0.995 0.875 0.930 0.775 0.898 1.140 0.928 1.322 10 1.018 1.051