A geneticist recovered 250 progeny with phenotype A and 150 with phenotype B from a cross she was scoring. Null hypothesis was that the data fit a 3:1 ratio. Calculate the Chi square value for that hypothesis.
To calculate the Chi square value for the given hypothesis, we need to follow these steps:
1. Set up the null hypothesis and alternative hypothesis:
- Null hypothesis (H0): The observed data fit a 3:1 ratio (expected ratio).
- Alternative hypothesis (Ha): The observed data do not fit a 3:1 ratio.
2. Determine the expected number of progeny for each phenotype based on the null hypothesis.
- For phenotype A (3:1 ratio), the expected number is (250 + 150) * (3/4) = 300.
- For phenotype B (3:1 ratio), the expected number is (250 + 150) * (1/4) = 100.
3. Calculate the Chi square value using the formula:
- Chi square (χ²) = Σ((Observed - Expected)² / Expected)
- Σ denotes the summation of each value calculated for each phenotype.
Let's calculate the Chi square value:
For phenotype A:
Observed (O1) = 250
Expected (E1) = 300
For phenotype B:
Observed (O2) = 150
Expected (E2) = 100
The Chi square value is calculated as follows:
Σ((O1 - E1)² / E1) + Σ((O2 - E2)² / E2)
= ((250 - 300)² / 300) + ((150 - 100)² / 100)
= (−50² / 300) + (50² / 100)
= (2500 / 300) + (2500 / 100)
= 8.33 + 25
= 33.33
Therefore, the Chi square value for the given hypothesis is 33.33.