Mathematics, 31.12.2019 02:31 stef65
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.
Answers: 2
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