Question 1202687: The National Turkey Association wants to experiment with the effects of three different feed mixtures on weight gain in poults. test at the .05 level the hypothesis that there is no effect of feed mixture on weight.
charts; weight(in pounds)
Feed Mixture A Feed Mixture B feed Mixture C
11.2(a) 12.6 (b) 11.3 (c)
12.1(a) 10.8 (b) 11.9(c)
10.9 (a) 11.3 (b) 12.4(c)
11.3 (a) 11.0 (b) 10.6(c)
12.0 (a) 12.0 (b) 12.0 (c)
10.7 (b)
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website! To test the hypothesis that the feed mixture has no effect on the weight of poults at the \( \alpha = 0.05 \) significance level, we will use **ANOVA (Analysis of Variance)**. This method tests whether there are significant differences among the means of multiple groups.
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### **Steps for ANOVA:**
1. **Null and Alternative Hypotheses**:
- \( H_0 \): There is no significant difference in the means of the weights for the three feed mixtures.
- \( H_a \): At least one feed mixture produces a significantly different mean weight.
2. **Data**:
The weights for each feed mixture are given:
- Feed Mixture A: \( 11.2, 12.1, 10.9, 11.3, 12.0 \)
- Feed Mixture B: \( 12.6, 10.8, 11.3, 11.0, 12.0, 10.7 \)
- Feed Mixture C: \( 11.3, 11.9, 12.4, 10.6, 12.0 \)
3. **Descriptive Statistics**:
- Calculate the means and variances for each group.
- Compute the overall mean.
4. **ANOVA Table**:
- **Between-group variability (SSB)**: Measures how much the group means differ from the overall mean.
- **Within-group variability (SSW)**: Measures the variance within each group.
- Calculate the F-statistic:
\[
F = \frac{\text{Mean Square Between Groups (MSB)}}{\text{Mean Square Within Groups (MSW)}}
\]
- Compare the F-statistic with the critical value from the F-distribution table for \( \alpha = 0.05 \).
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### **Calculation**:
Let me compute the ANOVA table and perform the test.
### **ANOVA Results:**
1. **Sum of Squares**:
- Between Groups (\( \text{SSB} \)): \( 0.1574 \)
- Within Groups (\( \text{SSW} \)): \( 5.8920 \)
2. **Mean Squares**:
- Between Groups (\( \text{MSB} \)): \( 0.0787 \)
- Within Groups (\( \text{MSW} \)): \( 0.4532 \)
3. **F-Statistic**: \( F = 0.174 \)
4. **Critical Value** (\( F_{\text{critical}} \) at \( \alpha = 0.05 \)): \( 3.806 \)
5. **p-Value**: \( 0.843 \)
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### **Conclusion**:
Since the calculated \( F \)-statistic (\( 0.174 \)) is less than the critical value (\( 3.806 \)) and the p-value (\( 0.843 \)) is greater than \( \alpha = 0.05 \), we fail to reject the null hypothesis.
### **Interpretation**:
There is no significant evidence to suggest that the feed mixture has an effect on the weight gain of poults.
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