12. A cross is made between a blue and a red strain of cabbage. The offspring are green, and when these are self-fertilized, the progeny are 225 blue, 472 green and 230 red cabbage plants. Using chi square analysis, test the hypothesis that these results are consistent with a hypothesis of incomplete dominance. What is the expected value for the green cabbage?
a. 231.75
b. 463.5
c. 58.69
d. 927
e. 695.25
e. 695.25
Hmmm, let me crunch some numbers while juggling some cabbages. 🤹♂️
To determine the expected value for the green cabbage, we need to use chi-square analysis. We can calculate the expected value using the formula: expected value = (total number of offspring) x (probability of green).
Now, let's perform some mathematical acrobatics:
Total number of offspring = blue + green + red = 225 + 472 + 230 = 927.
Since the cross between blue and red strains results in green cabbage, and we're considering incomplete dominance, the probability of getting a green cabbage is 1/2.
Expected value = 927 x 1/2 = 463.5.
So, the expected value for the green cabbage is 463.5, option b.
Now, if you excuse me, I have to go juggle some cabbages in celebration. 🥬🤡🥬
To test the hypothesis that the results are consistent with a hypothesis of incomplete dominance, we can use a chi-square analysis. The chi-square test compares the observed frequencies of different phenotypes (in this case, blue, green, and red cabbage plants) with the expected frequencies.
The expected frequencies can be calculated using the following formula:
Expected frequency = (total number of plants) * (proportion of the phenotype)
First, let's calculate the expected values for each phenotype:
Blue cabbage:
Expected frequency = (total number of plants) * (proportion of blue cabbage)
Expected frequency = (225 + 472 + 230) * (1/4) = 927/4 = 231.75
Green cabbage:
Expected frequency = (total number of plants) * (proportion of green cabbage)
Expected frequency = (225 + 472 + 230) * (1/2) = 927/2 = 463.5
Red cabbage:
Expected frequency = (total number of plants) * (proportion of red cabbage)
Expected frequency = (225 + 472 + 230) * (1/4) = 927/4 = 231.75
Therefore, the expected value for the green cabbage is 463.5 (option b).
To test the hypothesis of incomplete dominance in this cross, we can use the chi-square analysis. The chi-square test compares the observed data with the expected data to determine if there is a significant difference between the observed and expected values.
To calculate the expected values, we need to determine the proportions of each phenotype in the cross based on the assumption of incomplete dominance. In incomplete dominance, the heterozygous genotype results in an intermediate phenotype, which in this case is green.
Let's denote the blue strain as BB, the red strain as RR, and the green strain as BR (heterozygous). Based on incomplete dominance, the offspring of BB and RR will be BR.
Now, let's calculate the expected values for each phenotype:
1. Blue cabbage plants:
The blue strain (BB) is purebred, so all offspring from self-fertilization will be blue.
Expected number of blue plants = (blue progeny / total progeny) * total blue progeny
Expected number of blue plants = (225 / 927) * (225 + 472 + 230)
Expected number of blue plants = (0.2429718) * 927
Expected number of blue plants ≈ 225.06
2. Green cabbage plants:
The green strain (BR) results from the cross between blue (BB) and red (RR), so all the progeny from self-fertilized green plants (BR) will be green.
Expected number of green plants = (green progeny / total progeny) * total green progeny
Expected number of green plants = (472 / 927) * (225 + 472 + 230)
Expected number of green plants = (0.508124) * 927
Expected number of green plants ≈ 470.94
3. Red cabbage plants:
The red strain (RR) is purebred, so all offspring from self-fertilization will be red.
Expected number of red plants = (red progeny / total progeny) * total red progeny
Expected number of red plants = (230 / 927) * (225 + 472 + 230)
Expected number of red plants = (0.2489043) * 927
Expected number of red plants ≈ 230
Now that we have calculated the expected values, we can perform the chi-square analysis to determine if the observed and expected values differ significantly. However, the question only asks for the expected value for green cabbage, which is approximately 470.94.
Therefore, the correct answer is b. 463.5.