From the data given we find that the temperature and ph level remains the same for all days. Hence there cannot be any variation due to these elements.
Tank I and Tank 2: Group I
Tank 3 and Tank 4: Group II
The factor is the comparison of difference in oxygen levels after feeding.
Group I average oxygen level before food = 8.27
Group II average oxygen level before food = 8.117
Group I average oxygen level after food = 8.6349
Group II average oxygen level after food = 8.6383
Difference in oxygen level for group I = 8.6349-8.27 = 0.3649
Difference in oxygen level for group II = 8.6383-8.117 = 0.5213
H0: There is no change in oxygen level because of protein food
Ha: There is decrease in oxygen level because fish take more oxygen after protein food.
One tailed test for difference in oxygen level.
Significance level = 0.05 (say)
Var of group I = Var before food+ variance after food for tank 1 and 2
= 0.00056+0.09305 = 0.09361
Number n = 40
Variance of group II = 0.0930+0.0988 = 0.1918
Conclusion: Since p value is not less than 0.05 there is no statistical evidence of association of protein food to increase consumption of oxygen by fish.
II Paired t test:
H0: UD = U1 – U2 = 0, where UD equals the mean of the population of difference scores across the two measurements.
Ha: UD not equals 0.
T = -0.1564/
P = 0.495
Since p > 0.05, we accept null hypothesis that the differences in the two difference levels of oxygen are almost zero.
III) Anova test:
H0: There is no association between treatments and control
Ha: There is association between the two.
F = 555.384 and p =0.00
Since p <0.05 reject null hypothesis.
There is no association between protein food and oxygen intake.
Note: We get the same conclusion in all the three test.
Excel sheet is enclosed which calculated mean, Std deviation and the data taken is the first day of tank 1 and 2 before food, and last day of tank 1, tank 2 after food
And similarly for tank3 and 4.