One of the characters Mendel studied was the position of the flowers. He crossed plants
that had flowers at the tips of the stems with plants that had flowers along the sides. He
allowed the F1 plants, which had flowers along the sides, to self-fertilize. In the F2
generation, he counted 651 plants with stems on the sides and 207 with stems at the tips.
a. What is the chi-square value under the null hypothesis of 3:1 segregation?
To calculate the chi-square value under the null hypothesis of 3:1 segregation, you need to follow these steps:
1. Set up the null hypothesis: In this case, the null hypothesis states that the ratio of plants with stems at the tips to plants with stems on the sides is 3:1, as expected.
2. Calculate the expected number of plants with stems at the tips and on the sides: Since the expected ratio is 3:1, you need to determine the total number of plants and divide it into these two categories. For example, if we assume there are 858 plants in the F2 generation (651 + 207), you would expect 3/4 (or 0.75) of them to have stems on the sides and 1/4 (or 0.25) to have stems at the tips.
- Expected number of plants with stems on the sides: 0.75 * 858 = 643.5
- Expected number of plants with stems at the tips: 0.25 * 858 = 214.5
3. Set up the chi-square formula: The chi-square formula is Χ² = Σ((O - E)² / E), where Χ² is the chi-square value, Σ represents summation, O is the observed frequency, and E is the expected frequency.
4. Calculate the chi-square value: Substitute the observed and expected frequencies into the formula and sum up the results.
Χ² = ((651 - 643.5)² / 643.5) + ((207 - 214.5)² / 214.5)
Calculate this expression to get the chi-square value.
5. Finally, look up the chi-square value in a chi-square distribution table with appropriate degrees of freedom to determine the significance level or p-value associated with the chi-square test. This will give you information on whether to reject or fail to reject the null hypothesis.
Note that the degrees of freedom can be found using the formula: DF = (number of categories - 1) = 2 - 1 = 1