How do nematodes (microscopic worms) affect plant growth? a botanist prepares 16 identical

planting pots and then introduces different numbers of nematodes into the pots. four pots get 0

nematodes, four get 1,000, four get 5,

000, and four get 10,000. a tomato seedling is

transplanted into each pot. seedlings are assigned to pots (i. e., to treatments) by a completely

randomized design. below are the data on the increase in height of the seedlings in centimeters

16 days after planting.

nematodes seedling growth

0 10.8 9.1 12.5 9.2

1000 11.1 10.4 8.2 11.3

5000 5.4 4.6 7.4 5.2

1 5.8 5.3 3.2 7.5

a. for each pair of treatments, conduct a two

-sample t test to determine whether there are

significant differences in the mean seedling growth. assume that the data from each treatment

are a sample from a normal distribution with unknown mean and variance. further assume that

the variances for the four treatments are all equal.

each test should be conducted at the 0.05 level. you should end up doing 6 tests in order to

compare all possible pairs. you should use statistical software to do the tests. select the option

that assumes equal variances.

which treatments appear to differ? what is

your overall conclusion?

b. repeat the above, but now do not assume that the variances for the four treatments are all equal.

note:

when using jmp to analyze the

data, you will need to enter the data in six pairs of

columns (one pair for each pair of treatments you want to compare) of the form

growth1 nematode1 growth2 nematode2 etc.

10.8 0 10.8 0

9.1 0 9.1 0

12.5 0 12.5 0

9.2 0 9.2 0

11.1 1000 5.4 5000

10.4 1000 4.6 5000

8.2 1000 7.4 5000

11.3 1000 5.2 5000

thus, you will end up typing in 6 pairs of columns. you will also need to designate the

nematode variables as nominal. then select analyze from the menu and choose fit y by x.

this brings up a dialog box. select the appropriate growth column for the y response and the

corresponding nematode column for the x factor. click ok. this produces a plot. click on the

small red arrow in the upper left corner (by the title "oneway analysis of ") and select

means/anova/pooled t to compare means under the assumption that the variances are equal.

select t test to compare the means under the assumption that the variances are not equal.