A botanist wants to determine the effect of microscopic worms on seedling growth. He prepares 16 identical planting pots and then introduces four sets of worm populations into them. There are four groups of pots with four pots in each group. The worm population group sizes are 0 (intro- duced into the first group of four pots), 500 (introduced into the second group of four pots), 1000 (introduced into the third group of four pots), and 4000 (introduced into the fourth group of four pots). Two weeks after planting, he measures the seedling growth in centimeters. The results are given in the table below.
Seedling Growth in Centimeters by Worm Population Group
|
Group 1
(0 worms)
|
Group 2
(500 worms)
|
Group 3
(1000 worms)
|
Group 4
(4000 worms)
|
|
10.7
|
11.1
|
5.7
|
4.7
|
|
9.0
|
11.1
|
5.1
|
3.2
|
|
13.4
|
8.9
|
7.2
|
6.5
|
|
9.2
|
11.4
|
4.8
|
5.3
|
a. State the null hypothesis and determine the ANOVA table.
b. What is the result of the F test?
c. Apply Tukey's HSD test to see which means differ if the ANOVA was significant at the 5% level.