Let's look at the data in detail:
Predicted fractions and percentages:
1. Black Fur and Black Eyes:
- Fraction: [tex]\( \frac{9}{16} = 0.5625 \)[/tex]
- Percentage: [tex]\( 56.25\% \)[/tex]
2. Black Fur and Red Eyes:
- Fraction: [tex]\( \frac{3}{16} = 0.1875 \)[/tex]
- Percentage: [tex]\( 18.75\% \)[/tex]
3. White Fur and Black Eyes:
- Fraction: [tex]\( \frac{3}{16} = 0.1875 \)[/tex]
- Percentage: [tex]\( 18.75\% \)[/tex]
4. White Fur and Red Eyes:
- Fraction: [tex]\( \frac{1}{16} = 0.0625 \)[/tex]
- Percentage: [tex]\( 6.25\% \)[/tex]
Laboratory fractions and percentages:
1. Black Fur and Black Eyes:
- Fraction: [tex]\( \frac{155}{250} = 0.62 \)[/tex]
- Percentage: [tex]\( 62\% \)[/tex]
2. Black Fur and Red Eyes:
- Fraction: [tex]\( \frac{51}{250} = 0.204 \)[/tex]
- Percentage: [tex]\( 20.4\% \)[/tex]
3. White Fur and Black Eyes:
- Fraction: [tex]\( \frac{44}{250} = 0.176 \)[/tex]
- Percentage: [tex]\( 17.6\% \)[/tex]
4. White Fur and Red Eyes:
- Fraction: [tex]\( \frac{20}{250} = 0.08 \)[/tex]
- Percentage: [tex]\( 8.0\% \)[/tex]
The predicted values and laboratory results do not match. The predicted values represent what should theoretically occur under ideal conditions based on specific genetic models or expected outcomes. When comparing these values to the laboratory results, discrepancies arise.
Reason for Differences:
The differences between the predicted percentages and laboratory percentages most likely result from:
1. Random Sampling Variability: When dealing with any sample (in this case, 250 mice), there can be variations from the predicted values due to the randomness inherent in sampling. This means that in a smaller number of observations, the actual sampled offspring ratios may deviate from the theoretical expectations.
2. Experimental Error: Possible errors or variations in the experimental setup or methodology could result in differences. These might include inconsistencies in breeding, record-keeping errors, or misclassification of traits.
3. Genetic Variation: There might be additional genetic factors or mutations that deviate from the simple model used to predict the fractions.
Thus, the disparities observed in these percentages most likely result from random sampling variability or experimental error in the laboratory results.
