Matthew collected the following data: Table 4.1 Effect of Diazinon Exposure on T
ID: 305116 • Letter: M
Question
Matthew collected the following data:
Table 4.1 Effect of Diazinon Exposure on Tadpole Length
Tadpole length (cm)
Control
0.25 ppb
0.5 ppb
1.0 ppb
Tadpole 1
4.4
4.4
3.1
3.5
Tadpole 2
4.6
3.5
3.4
3.1
Tadpole 3
4.2
3.8
3.7
2.8
Tadpole 4
3.8
4.2
4.0
3.3
Tadpole 5
4.3
4.1
3.3
2.6
Mean (cm)
4.26
4.0
3.5
3.06
Std Dev (cm)
0.3
0.4
0.4
0.4
t-test probability
(p-value)
NA
0.122
0.003
0.0002
Based on the data presented in the table above, are any of the treatment groups significantly different from the control group? If so, which groups are different and how do you know they are different?
Tadpole length (cm)
Control
0.25 ppb
0.5 ppb
1.0 ppb
Tadpole 1
4.4
4.4
3.1
3.5
Tadpole 2
4.6
3.5
3.4
3.1
Tadpole 3
4.2
3.8
3.7
2.8
Tadpole 4
3.8
4.2
4.0
3.3
Tadpole 5
4.3
4.1
3.3
2.6
Mean (cm)
4.26
4.0
3.5
3.06
Std Dev (cm)
0.3
0.4
0.4
0.4
t-test probability
(p-value)
NA
0.122
0.003
0.0002
Explanation / Answer
1) For 0.25 ppb
sample size(n)=5
Sample mean(m)=4
Controlled population mean(q)=4.26
Sample standard deviation(s)=0.4
Control population standard deviation(S)=0.3
S, the t value is
=l m-q l / ?{(S/n)2+(s/n)2}
=2.6
for 5 samples degrees of freedom is
=2n-2=8
as the two populations can be related in both positive and negative way so a two tailed test has to be conducted
For df of 8 and p value of .122 critical value is 1.860
So, t value>critical value
So, the population is significantly different
2) For 0.5 ppb population
t=7.6 Critical value is 4.501
So, t>critical value
3) For 1 ppb
t=12 critical value 6.44
so the population is significantly different