Model Answer
0 min readIntroduction
Gregor Mendel’s laws of inheritance, established through his experiments with pea plants, form the foundation of modern genetics. These laws predict specific phenotypic ratios in offspring resulting from genetic crosses. However, deviations from these expected ratios can occur due to chance or other factors. The Chi-square test is a statistical tool used to assess the goodness of fit between observed and expected frequencies, allowing us to determine if observed deviations are statistically significant. In this case, we will use the Chi-square test with a significance level of P = 5% to evaluate whether the observed segregation of pod colour in pea plants aligns with the expected 3:1 ratio.
Understanding the Chi-Square Test
The Chi-square test (χ²) is a statistical test used to determine if there is a significant association between two categorical variables. In genetics, it’s commonly used to compare observed phenotypic ratios with expected Mendelian ratios. The formula for the Chi-square statistic is:
χ² = Σ [(Oi - Ei)² / Ei]
Where:
- Oi = Observed frequency for each category
- Ei = Expected frequency for each category
- Σ = Summation across all categories
Step 1: Formulating Hypotheses
Null Hypothesis (H0): The observed segregation ratio of green and yellow pod colours (787:277) is consistent with the expected 3:1 ratio.
Alternative Hypothesis (H1): The observed segregation ratio of green and yellow pod colours is not consistent with the expected 3:1 ratio.
Step 2: Constructing the Contingency Table
First, we need to calculate the total number of individuals observed: 787 (green) + 277 (yellow) = 1064.
Based on the 3:1 ratio, the expected number of individuals for each phenotype is:
- Expected Green: (3/4) * 1064 = 798
- Expected Yellow: (1/4) * 1064 = 266
Now, we can construct the contingency table:
| Phenotype | Observed (Oi) | Expected (Ei) |
|---|---|---|
| Green | 787 | 798 |
| Yellow | 277 | 266 |
| Total | 1064 | 1064 |
Step 3: Calculating the Chi-Square Statistic
Using the formula, we calculate the Chi-square statistic:
χ² = [(787 - 798)² / 798] + [(277 - 266)² / 266]
χ² = [(-11)² / 798] + [(11)² / 266]
χ² = [121 / 798] + [121 / 266]
χ² = 0.151 + 0.455
χ² = 0.606
Step 4: Determining Degrees of Freedom and Critical Value
Degrees of freedom (df) = Number of categories - 1. In this case, df = 2 - 1 = 1.
With a significance level (P) of 5% and 1 degree of freedom, the critical value from the Chi-square distribution table is 3.841.
Step 5: Interpreting the Results
Since the calculated Chi-square statistic (0.606) is less than the critical value (3.841), we fail to reject the null hypothesis.
This indicates that the observed segregation ratio of green and yellow pod colours is not significantly different from the expected 3:1 ratio at the 5% significance level.
Conclusion
In conclusion, the Chi-square test results demonstrate that the observed segregation of pod colour in the pea plant cross (787 green, 277 yellow) does not significantly deviate from the expected 3:1 Mendelian ratio at a P = 5% significance level. Therefore, we accept the null hypothesis, suggesting that the observed results are consistent with Mendelian inheritance principles. Further studies with larger sample sizes could provide even more robust evidence.
Answer Length
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