1. To study variation in income from state to state, researchers obtained a
random sample of 5 states, and sampled median income from 5 counties in each
state. The data are listed below.
1) Complete the ANOVA table and conduct a test of whether sigma
a2
= 0.
2) Estimate the variance components for states and counties.
3) Calculate the estimate of intraclass correlation.
state median income (in thousands) California 51.564 California 44.102 California 57.647 California 70.247 California 61.985 Iowa 42.384 Iowa 46.994 Iowa 48.467 Iowa 35.035 Iowa 47.130 Missouri 51.476 Missouri 38.530 Missouri 34.007 Missouri 33.980 Missouri 32.620 Ohio 38.110 Ohio 45.659 Ohio 34.359 Ohio 41.672 Ohio 39.792 Vermont 52.135 Vermont 60.182 Vermont 51.993 Vermont 39.914 Vermont 46.912
2. Use the data from the meat storage experiment (in display 2.1) to determine how many samples would be needed in each group in a future experiment to the reject the null hypothesis at the .05 level of significance with power of at least .9, if the mean log counts in the four groups were 7, 6.5, 6, and 6.5.