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Sagot :
Certainly! Let's analyze the given data step by step, starting with the observed and predicted frequencies. We'll also determine the absolute and percentage differences between them.
### Step 1: Observed Frequencies
The observed frequencies are as given:
- Black Fur and Black Eyes: 155
- Black Fur and Red Eyes: 51
- White Fur and Black Eyes: 44
- White Fur and Red Eyes: 20
### Step 2: Predicted Fractions
The predicted fractions for each category are:
- Black Fur and Black Eyes: [tex]\( \frac{9}{16} \)[/tex]
- Black Fur and Red Eyes: [tex]\( \frac{3}{16} \)[/tex]
- White Fur and Black Eyes: [tex]\( \frac{3}{16} \)[/tex]
- White Fur and Red Eyes: [tex]\( \frac{1}{16} \)[/tex]
### Step 3: Predicted Frequencies
Given the total count of offspring mice is 250, the predicted frequencies for each category are calculated as follows:
- Black Fur and Black Eyes: [tex]\( 250 \times \frac{9}{16} = 140.625 \)[/tex]
- Black Fur and Red Eyes: [tex]\( 250 \times \frac{3}{16} = 46.875 \)[/tex]
- White Fur and Black Eyes: [tex]\( 250 \times \frac{3}{16} = 46.875 \)[/tex]
- White Fur and Red Eyes: [tex]\( 250 \times \frac{1}{16} = 15.625 \)[/tex]
### Step 4: Differences Between Observed and Predicted Frequencies
We calculate the differences for each category:
1. Black Fur and Black Eyes:
- Observed: 155
- Predicted: 140.625
- Difference: [tex]\( 155 - 140.625 = 14.375 \)[/tex]
2. Black Fur and Red Eyes:
- Observed: 51
- Predicted: 46.875
- Difference: [tex]\( 51 - 46.875 = 4.125 \)[/tex]
3. White Fur and Black Eyes:
- Observed: 44
- Predicted: 46.875
- Difference: [tex]\( 44 - 46.875 = -2.875 \)[/tex]
4. White Fur and Red Eyes:
- Observed: 20
- Predicted: 15.625
- Difference: [tex]\( 20 - 15.625 = 4.375 \)[/tex]
### Step 5: Differences as Percentages of the Total Population
To better understand the differences, we convert them into percentages relative to the total count of 250 offspring:
1. Black Fur and Black Eyes:
- Difference: 14.375
- Percentage difference: [tex]\( \frac{14.375}{250} \times 100 = 5.75 \% \)[/tex]
2. Black Fur and Red Eyes:
- Difference: 4.125
- Percentage difference: [tex]\( \frac{4.125}{250} \times 100 = 1.65 \% \)[/tex]
3. White Fur and Black Eyes:
- Difference: -2.875
- Percentage difference: [tex]\( \frac{-2.875}{250} \times 100 = -1.15 \% \)[/tex]
4. White Fur and Red Eyes:
- Difference: 4.375
- Percentage difference: [tex]\( \frac{4.375}{250} \times 100 = 1.75 \% \)[/tex]
### Summary
From the analysis, the absolute differences are:
- 14.375 (5.75%) more mice with Black Fur and Black Eyes were observed compared to predictions.
- 4.125 (1.65%) more mice with Black Fur and Red Eyes were observed compared to predictions.
- 2.875 (-1.15%) fewer mice with White Fur and Black Eyes were observed compared to predictions.
- 4.375 (1.75%) more mice with White Fur and Red Eyes were observed compared to predictions.
These differences between the predicted and observed percentages may result from random variations inherent in biological experiments or slight experimental errors in the lab.
By following this detailed breakdown, we can see how the given data leads to the final differences and understand the calculations behind the percentages presented.
### Step 1: Observed Frequencies
The observed frequencies are as given:
- Black Fur and Black Eyes: 155
- Black Fur and Red Eyes: 51
- White Fur and Black Eyes: 44
- White Fur and Red Eyes: 20
### Step 2: Predicted Fractions
The predicted fractions for each category are:
- Black Fur and Black Eyes: [tex]\( \frac{9}{16} \)[/tex]
- Black Fur and Red Eyes: [tex]\( \frac{3}{16} \)[/tex]
- White Fur and Black Eyes: [tex]\( \frac{3}{16} \)[/tex]
- White Fur and Red Eyes: [tex]\( \frac{1}{16} \)[/tex]
### Step 3: Predicted Frequencies
Given the total count of offspring mice is 250, the predicted frequencies for each category are calculated as follows:
- Black Fur and Black Eyes: [tex]\( 250 \times \frac{9}{16} = 140.625 \)[/tex]
- Black Fur and Red Eyes: [tex]\( 250 \times \frac{3}{16} = 46.875 \)[/tex]
- White Fur and Black Eyes: [tex]\( 250 \times \frac{3}{16} = 46.875 \)[/tex]
- White Fur and Red Eyes: [tex]\( 250 \times \frac{1}{16} = 15.625 \)[/tex]
### Step 4: Differences Between Observed and Predicted Frequencies
We calculate the differences for each category:
1. Black Fur and Black Eyes:
- Observed: 155
- Predicted: 140.625
- Difference: [tex]\( 155 - 140.625 = 14.375 \)[/tex]
2. Black Fur and Red Eyes:
- Observed: 51
- Predicted: 46.875
- Difference: [tex]\( 51 - 46.875 = 4.125 \)[/tex]
3. White Fur and Black Eyes:
- Observed: 44
- Predicted: 46.875
- Difference: [tex]\( 44 - 46.875 = -2.875 \)[/tex]
4. White Fur and Red Eyes:
- Observed: 20
- Predicted: 15.625
- Difference: [tex]\( 20 - 15.625 = 4.375 \)[/tex]
### Step 5: Differences as Percentages of the Total Population
To better understand the differences, we convert them into percentages relative to the total count of 250 offspring:
1. Black Fur and Black Eyes:
- Difference: 14.375
- Percentage difference: [tex]\( \frac{14.375}{250} \times 100 = 5.75 \% \)[/tex]
2. Black Fur and Red Eyes:
- Difference: 4.125
- Percentage difference: [tex]\( \frac{4.125}{250} \times 100 = 1.65 \% \)[/tex]
3. White Fur and Black Eyes:
- Difference: -2.875
- Percentage difference: [tex]\( \frac{-2.875}{250} \times 100 = -1.15 \% \)[/tex]
4. White Fur and Red Eyes:
- Difference: 4.375
- Percentage difference: [tex]\( \frac{4.375}{250} \times 100 = 1.75 \% \)[/tex]
### Summary
From the analysis, the absolute differences are:
- 14.375 (5.75%) more mice with Black Fur and Black Eyes were observed compared to predictions.
- 4.125 (1.65%) more mice with Black Fur and Red Eyes were observed compared to predictions.
- 2.875 (-1.15%) fewer mice with White Fur and Black Eyes were observed compared to predictions.
- 4.375 (1.75%) more mice with White Fur and Red Eyes were observed compared to predictions.
These differences between the predicted and observed percentages may result from random variations inherent in biological experiments or slight experimental errors in the lab.
By following this detailed breakdown, we can see how the given data leads to the final differences and understand the calculations behind the percentages presented.
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