A study was conducted to compare the effect of three levels of digitalis on the level of calcium in the heart muscle of dogs. A description of the actual experimental procedure is omitted, but it is sufficient to note that the general level of calcium uptake varies from one animal to another so that comparison of digitalis levels (treatments) had to be blocked on heart muscles. That is, the tissue for a heart muscle was regarded as a block and comparisons of the three treatments were made within a given muscle. The calcium uptakes for the three levels of digitalis, A, B, and C, were compared based on the heart muscles of four dogs. The results are shown in the accompanying table.
| Dogs |
| 1 |
2 |
3 |
4 |
| A |
B |
C |
D |
| 1342 |
1698 |
1296 |
1150 |
| B |
B |
A |
C |
| 1608 |
1387 |
1029 |
1579 |
| C |
A |
C |
B |
| 1881 |
1140 |
1549 |
1319 |
a Calculate the sums of squares for this experiment and construct an ANOVA table.
b How many degrees of freedom are associated with SSE?
c Do the data present sufficient evidence to indicate a difference in the mean uptake of calcium for the three levels of digitalis?
d Do the data indicate a difference in the mean uptake in calcium for the heart muscles of the four dogs?
e Give the standard deviation of the difference between the mean calcium uptakes for two levels of digitalis.
f Find a 95% confidence interval for the difference in mean responses between treatments A and B.