The data for this question comes from gauge repeatability and reproducibility (gage R&R) experiments. In this case, twenty parts were measured by three different operators. Each part was measured twice by each operator, and the operators were the same for the whole experiment. We want to determine the variance components in this experiment.

1. Write down the equation for this experiment and state explicitly the assumptions you make about the different terms. Include the equations for the variance components and explain how they can be estimated.
2. Fit a model using the method of moments and comment on the results. Is there anything improper about this model?
3. Fit a model using the lmer function and interpret the results. Compare with the model you fitted in (b) and comment.
4. Using the method described in class, get a 95% confidence interval for the variance component for the operator.