### Solution
#### 1.1 State the sample size of this investigation:
The sample size is the total number of rats involved in the investigation. Each group has 3 rats, and there are 3 groups.
Therefore, the total sample size is:
[tex]\[ 3 \, \text{rats/group} \times 3 \, \text{groups} = 9 \, \text{rats} \][/tex]
So, the sample size is 9.
#### 1.2 Calculate the average mass of (i), (ii) and (iii):
To find the average mass of each group before and after 3 weeks, follow these steps:
(i) Calculate the average mass of Diet X:
- The initial average mass is given as 319 grams.
- The final masses after 3 weeks for Rat 1 is 320 grams.
Since there is only one final mass provided for Diet X group:
[tex]\[ \text{Average mass of group (i)} = \frac{\text{Initial average mass + Total final masses}}{\text{Number of initial values + Number of final values}} \][/tex]
[tex]\[ \text{Average mass of group (i)} = \frac{319 + 320}{1 + 1} = \frac{639}{2} = 319.5 \, \text{grams} \][/tex]
(ii) Calculate the average mass of Diet Y:
- The initial average mass is given as 32 grams.
- Final masses after 3 weeks for three rats are: 305 grams, 31 grams, and 3 grams.
[tex]\[ \text{Average mass of group (ii)} = \frac{\text{Initial average mass + Total final masses}}{\text{Number of initial values + Number of final values}} \][/tex]
[tex]\[ \text{Average mass of group (ii)} = \frac{32 + 305 + 31 + 3}{1 + 3} = \frac{371}{4} = 92.75 \, \text{grams} \][/tex]
(iii) Calculate the average mass of Diet Z:
- The initial average mass is given as 318 grams.
- Final masses after 3 weeks for three rats are: 345 grams, 338 grams, and 337 grams.
[tex]\[ \text{Average mass of group (iii)} = \frac{\text{Initial average mass + Total final masses}}{\text{Number of initial values + Number of final values}} \][/tex]
[tex]\[ \text{Average mass of group (iii)} = \frac{318 + 345 + 338 + 337}{1 + 3} = \frac{1338}{4} = 334.5 \, \text{grams} \][/tex]
#### 1.3 Which group has the highest average mass after 3 weeks:
To determine the group with the highest average mass after 3 weeks, compare the average mass of each group:
- Group (i) average mass: [tex]\( 319.5 \, \text{grams} \)[/tex]
- Group (ii) average mass: [tex]\( 92.75 \, \text{grams} \)[/tex]
- Group (iii) average mass: [tex]\( 334.5 \, \text{grams} \)[/tex]
The group with the highest average mass after 3 weeks is Group (iii) with 334.5 grams.
