I'm sorry but I had to post this question again as I left out the question. In a certain species of plant, the allele to produce green melons (G) is
dominant over the allele to produce yellow melons (g). A student performed a cross
between a plant that produced green melons and a plant that produced yellow melons.
When the student observed the next generation, the 94 seeds that were produced from the
cross matured into 53 plants with green melons and 41 plants with yellow melons. Calculate the chi-squared value for the null hypothesis that the green-melon parent was heterogeneous for the melon-color gene.
To calculate the chi-squared value for the given scenario, we can use the following steps:
1. Determine the observed and expected values for each phenotype (green and yellow melons).
The observed values are 53 plants with green melons and 41 plants with yellow melons.
To calculate the expected values, we need to assume that the green-melon parent is heterozygous (Gg) for the melon-color gene. This means that in the next generation, we would expect a 1:1 ratio of green and yellow melon phenotypes.
So, the expected values would be:
- Expected green melons: (94 seeds / 2) = 47 plants
- Expected yellow melons: (94 seeds / 2) = 47 plants
2. Calculate the chi-squared value using the formula:
Chi-squared = Σ [(Observed - Expected)^2 / Expected]
For each phenotype, the calculation would be as follows:
- (53 - 47)^2 / 47 = 0.2553
- (41 - 47)^2 / 47 = 0.2553
3. Sum up the chi-squared values for each phenotype:
Chi-squared = 0.2553 + 0.2553 = 0.5106
Therefore, the chi-squared value for the null hypothesis that the green-melon parent was heterogeneous for the melon-color gene is 0.5106.
To calculate the chi-squared value for the given scenario, we need to follow these steps:
Step 1: Set up the null hypothesis and alternative hypothesis.
The null hypothesis (H0) states that the green-melon parent was heterogeneous for the melon-color gene, meaning it carried both the dominant (G) and recessive (g) alleles. The alternative hypothesis (Ha) would be that the green-melon parent was homozygous for the dominant (G) allele.
Step 2: Set up the expected frequencies for each phenotype.
Based on the laws of inheritance, we can determine the expected frequencies for each phenotype by assuming that the green-melon parent is heterozygous (Gg). The expected ratio is predicted to be 3:1, where three-fourths (75%) of the plants will have green melons (genotype ratio: GG or Gg) and one-fourth (25%) will have yellow melons (genotype ratio: gg).
According to the observed results:
- 53 plants had green melons, which is 53/94 = 0.5638 (56.38%) of the total.
- 41 plants had yellow melons, which is 41/94 = 0.4362 (43.62%) of the total.
So, we can calculate the expected frequencies:
- Expected green melon plants = 0.75 * 94 = 70.5
- Expected yellow melon plants = 0.25 * 94 = 23.5
Step 3: Calculate the chi-squared test statistic.
The formula to calculate the chi-squared test statistic is:
χ² = ∑((O - E)² / E)
Where:
- O = Observed frequency
- E = Expected frequency
Perform these calculations for each phenotype:
For green melon plants:
χ²_green = ((53 - 70.5)² / 70.5)
For yellow melon plants:
χ²_yellow = ((41 - 23.5)² / 23.5)
Step 4: Calculate the chi-squared value.
The chi-squared value is the sum of the calculated test statistics for each phenotype:
χ² = χ²_green + χ²_yellow
Finally, you can calculate the chi-squared value with the given formula.