The question involves determining which statement about the observed kiwis is true based on the given data. Let's analyze each statement step-by-step.
### Statement A: There were the most observations of female tokoeka kiwis.
1. Observations of female great spotted kiwis = 24
2. Observations of female Northland brown kiwis = 42
3. Observations of female tokoeka kiwis = 44
Among the female kiwis observed, the highest number of observations was of the tokoeka kiwis, with 44 observations.
### Statement B: Great spotted kiwis were more likely to be male than female.
1. Observations of male great spotted kiwis = 19
2. Observations of female great spotted kiwis = 24
3. Total observations of great spotted kiwis = 43 (Male 19 + Female 24)
To find which gender was more likely, we calculate the probabilities:
- Probability of a great spotted kiwi being male: [tex]\( \frac{19}{43} \)[/tex]
- Probability of a great spotted kiwi being female: [tex]\( \frac{24}{43} \)[/tex]
Since [tex]\( \frac{24}{43} \)[/tex] (female) is greater than [tex]\( \frac{19}{43} \)[/tex] (male), great spotted kiwis were more likely to be female than male. So, this statement is false.
### Statement C: More than half of the kiwis were Northland brown kiwis.
1. Total kiwis = 200
2. Observations of Northland brown kiwis = 81
To determine if more than half of the total kiwis were Northland brown:
- Fraction of Northland brown kiwis: [tex]\( \frac{81}{200} \)[/tex]
Calculating [tex]\( \frac{81}{200} \)[/tex] gives approximately 0.405, which is less than 0.5. So, this statement is false.
### Statement D: Northland brown kiwis were more likely to be female than tokoeka kiwis were.
1. Female Northland brown kiwis = 42
2. Total Northland brown kiwis = 81
3. Female tokoeka kiwis = 44
4. Total tokoeka kiwis = 76
To compare, we calculate the probabilities:
- Probability of a Northland brown kiwi being female: [tex]\( \frac{42}{81} \)[/tex]
- Probability of a tokoeka kiwi being female: [tex]\( \frac{44}{76} \)[/tex]
Calculating both:
- [tex]\( \frac{42}{81} \approx 0.519 \)[/tex]
- [tex]\( \frac{44}{76} \approx 0.579 \)[/tex]
Since [tex]\( 0.579 \)[/tex] (tokoeka) is greater than [tex]\( 0.519 \)[/tex] (Northland brown), tokoeka kiwis were more likely to be female than Northland brown kiwis. So, this statement is false.
Thus, the only true statement based on the observations and calculations is:
(A) There were the most observations of female tokoeka kiwis.
