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\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\multirow[b]{3}{}{ GROUP } & \multirow[b]{3}{}{\begin{tabular}{c}
DIET \\
(X, Y \\
or Z)
\end{tabular}} & \multicolumn{5}{|c|}{ Mass of rats [tex]$(g)$[/tex]} & \multirow[b]{3}{}{\begin{tabular}{c}
Average Oxygen \\
consumption \\
([tex]$ml / kg / min$[/tex])
\end{tabular}} \\
\cline{3-7}
& & \multirow{2}{}{\begin{tabular}{c}
Initial \\
Average \\
mass of \\
the three \\
rats (g)
\end{tabular}} & \multicolumn{4}{|c|}{ After 3 weeks } & \\
\cline{4-7}
& & & \begin{tabular}{c}
RAT \\
1 (g)
\end{tabular} & \begin{tabular}{c}
RAT \\
2 (g)
\end{tabular} & \begin{tabular}{c}
RAT \\
3 (g)
\end{tabular} & \begin{tabular}{c}
Average \\
mass of \\
rats (g)
\end{tabular} & \\
\hline
A & Diet X & 319 & 320 & & & (i) & 4 \\
\hline
B & 7 & 32 & 305 & 31 & 3 & (ii) & 10 \\
\hline
C & ? & 318 & 345 & 338 & 337 & (iii) & 2.7 \\
\hline
\end{tabular}

1.1 State the sample size of this investigation.
(1) [tex]$\square$[/tex]

1.2 Calculate the average mass of (i), (ii) and (iii).
(3) [tex]$\square$[/tex]

1.3 Which group has the highest average mass?
(1) [tex]$\square$[/tex]

Sagot :

GinnyAnsweridn
### 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.
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