Researchers cross a corn plant that is pure-breeding for...

Question

Researchers cross a corn plant that is pure-breeding for the dominant traits colored aleurone (C1), full kernel (Sh), and waxy endosperm (Wx) to a pure-breeding plant with the recessive traits colorless aleurone (c1), shrunken kernel (sh), and starchy (wx). The resulting F₁ plants were crossed to pure-breeding colorless, shrunken, starchy plants. Counting the kernels from about 30 ears of corn yields the following data.

Kernel Phenotype Number
Colored, shrunken, starchy 116
Colored, full, waxy 601
Colored, full, starchy 2538
Colored, shrunken, waxy 4
Colorless, shrunken, starchy 2708
Colorless, full, starchy 2
Colorless, full, waxy 113
Colorless, shrunken, waxy 626
6708

Perform a chi-square test to determine if these data show significant deviation from the expected phenotype distribution.

Accepted Answer

Welcome back everyone. Let's look at our next problem. It says If the F2 generation yields 60 individuals with a dominant phenotype and individuals with the recessive phenotype With the predicted ratio being 9 - 3 - four. What is the chi square value for a di hybrid cross between two genes showing epitasis? And our answer choices are a 9.9 B 15.9 C 19.9 and D 29.1. Well, we're given the number of offspring that we actually obtained and then we're given the predicted phenotypic ratio of the offspring and asked to calculate the chi square value. So let's recall our formula for chi square value. So we know where we need to start. And that formula says that chi squared equals the sum of. And then in parentheses, we have O minus E that difference squared divided by E and that's where O is the observed number of offspring or outcomes and then E is the expected number. So next, we want to calculate what would be the expected number of offspring since we're given uh how many we observed. So in this case, we start with our phenotypic ratio of 9-3-4, where nine would be the dominant phenotype. three would be an intermediate phenotype. So perhaps showing one dominant and one recessive trait. And then four would be the recessive phenotypes to calculate how many offspring we'd expect. We need to know the total number of offspring we obtained. So we're told we have 60 individuals with a DOIP phenotype and 28 with a recessive. So we need to add together 60 and 28. So we have 60 plus sign 28 equals 88 total individuals among the offspring. So to calculate our expected um numbers of offspring, we know we have nine out of 16 is our expected ratio are expected to percent with the dominant phenotype. And that would be times Well, that would be, excuse me, that would be multiplied by 88. And that's going to equal 49 0.5. Then for our intermediate phenotype, We have 3/16 Multiplied by 88 equals 16.5. And finally, for the recess phenotype for 16ths Multiplied by 88 equals 22. So those would be our expected numbers of offspring. So now we need to calculate our K squared value. So going back to our formula kai squared equals and now we're gonna sum up uh this value for each outcome in the phenotype. So for the first one, individuals with a dominant phenotype In parentheses, we have are observed minus expected so our observed offspring would be and then that's minus The expected number, which we said was 49.5. That difference is squared and divided by the expected number Should be 49.5. And again, our high score values the sum of these things. So now we say plus sign and for the next, the intermediate phenotype we have observed which is zero, we didn't get any offspring with the intermediate phenotype And then expected would be 16. that different squared divided by Expected number 16.5. And then we add to it, The final recessive phenotype observed would be 28. Then, So that's 28 as the observed number with recessive phenotype minus Our expected number, which is 22 that different squared. And then that's divided by The expected number, which would be 22. So now we have the three terms that are being added together and we calculate the K squared equals 2.12 plus sign 16. Plus 9, 1.27. And the sum of all three of those will equal 19.89. And when we go back to our answer choices, we see the choice C 19.9 will be our correct answer here. So that choice C 19.9 is the chi square value for a di hybrid cross between two genes showing epitasis in this episode that we're in this uh sample cross that we're given see you in the next video.

Key Concepts

Mendelian Genetics

Chi-Square Test

Phenotypic Ratios

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