Let's address the questions step-by-step to provide a detailed solution:
### 1.1 State the sample size of this investigation.
The sample size of an investigation refers to the total number of subjects used in the study. In this case, there are 3 rats per group, and there are 3 groups.
[tex]\[
\text{Sample size} = 3 \text{ (rats per group)} \times 3 \text{ (groups)} = 9 \text{ rats}
\][/tex]
### 1.2 Calculate the average mass of (i), (ii), and (iii).
To find the average mass, sum the masses of the rats in each group and divide by the number of rats in that group.
[tex]\[
i. \text{ Group A (Diet X)}: \text{Masses} = [320, 322, 322]
\][/tex]
[tex]\[
\text{Average mass of Group A} = \frac{320 + 322 + 322}{3} = \frac{964}{3} = 321.33 \text{ g} \quad (\text{rounded to 2 decimal places})
\][/tex]
[tex]\[
ii. \text{ Group B (Diet Y)}: \text{Masses} = [305, 315, 308]
\][/tex]
[tex]\[
\text{Average mass of Group B} = \frac{305 + 315 + 308}{3} = \frac{928}{3} = 309.33 \text{ g} \quad (\text{rounded to 2 decimal places})
\][/tex]
[tex]\[
iii. \text{ Group C (Diet Z)}: \text{Masses} = [345, 338, 337]
\][/tex]
[tex]\[
\text{Average mass of Group C} = \frac{345 + 338 + 337}{3} = \frac{1020}{3} = 340.00 \text{ g} \quad (\text{exact value})
\][/tex]
### 1.3 Which group has the highest average:
a) Oxygen consumption:
Group B has the highest average oxygen consumption of 10 ml/kg/min.
b) Average mass after three weeks:
Group C has the highest average mass after three weeks, which is 340.00 g.
### 1.4 What effect does an increase in thyroxin have on oxygen consumption?
An increase in thyroxin increases the metabolic rate, which in turn increases oxygen consumption.
### 1.5 Which group [tex]$( A , B$[/tex] or [tex]$C$[/tex] ) is the control in this investigation?
Usually, the control group is the one that has a normal diet and no experimental changes. Based on the data, Group A can be considered the control group since it has the normal average oxygen consumption and a diet marked as X.
### 1.6 Identify the diet [tex]$(X, Y$[/tex] or [tex]$Z$[/tex] ) used for:
a) Group B:
Given that Group B has the highest oxygen consumption (10 ml/kg/min), it suggests an increase in metabolic rate, potentially due to thyroxin. Therefore, Group B is likely on Diet Y.
b) Group [tex]$C$[/tex]:
Group C has an average oxygen consumption of 2.7 ml/kg/min, which suggests it is lower and more stable, indicating no experimental manipulation with thyroxin. Therefore, Group C is likely on Diet Z.
