An experienced goldfish breeder receives two unusual male goldfish. One is black rather than gold, and the other has a single tail fin rather than a split tail fin. The breeder crosses the black male to a female that is gold. All the F₁ are gold. She also crosses the single-finned male to a female with a split tail fin. All the F₁ have a split tail fin. She then crosses the black male to F₁ gold females and, separately, crosses the single-finned male to F₁ split-finned females. The results of the crosses are shown below.
Black male x F₁ gold female:
Gold 32
Black 34
Single-finned male x F₁ split-finned female:
Split fin 41
Single fin 39
Use chi-square analysis to test your hereditary hypothesis for each trait.

Question

An experienced goldfish breeder receives two unusual male goldfish. One is black rather than gold, and the other has a single tail fin rather than a split tail fin. The breeder crosses the black male to a female that is gold. All the F₁ are gold. She also crosses the single-finned male to a female with a split tail fin. All the F₁ have a split tail fin. She then crosses the black male to F₁ gold females and, separately, crosses the single-finned male to F₁ split-finned females. The results of the crosses are shown below.
  Black male x F₁ gold female:
    Gold         32
    Black        34
  Single-finned male x F₁ split-finned female:
    Split fin        41
    Single fin     39
Use chi-square analysis to test your hereditary hypothesis for each trait.

Black male x F₁ gold female:

Gold 32

Black 34

Single-finned male x F₁ split-finned female:

Split fin 41

Single fin 39

Use chi-square analysis to test your hereditary hypothesis for each trait.

Accepted Answer

Hi, everyone. Let's take a look at this practice problem together. A male mouse with black fur capital B, lowercase B was mated to a female mouse with white fur. Lowercase B. Lowercase B. The female produces a litter of 12 pups with seven black and five white fur. Determine the K square value for the fur color. The answer options are a 0.167 B 0.234 C 0.334 ND 0.667. Now recall that the chi square test is a statistical test that compares the observed and the expected outcomes for this problem. You must know the chi square formula and that formula is on the screen. The formula is chi squared equals the summation of open parentheses. O minus E closed parentheses squared divided by E where O is the observed value and E is the expected value. Now, this summation symbol in the equation tells us that we will need to solve the calculation for each trait for fur color and then add those values together. So to organize our information, we will use each table and that table is on the screen the first column is labeled class or the different fur colors. The second column is labeled observed o the third column is expected E and the fourth column is the chi square calculation for the first column class. We know that the two types of fur color are black and white. So we can fill that part of the table out. We'll put black fur in the first row and white fur in the second row. In the question, we are given the observed values for each for color. There was seven black fur pups and five white fur pups. So we'll enter those values into their respective spots on the table. The next step is to determine the expected outcome in order to fill out this third column in the table for this question, that's the expected outcome of the cross between the male mouse with the female mouse. And so that will be a cross between a black fur heterozygous male with the white fur homozygous recessive female. Now, the completed putt square of that cross is on the screen. The male alleles are in the top row, capital B, lowercase B and the female ails, lowercase B, lowercase B are in the first column of the puit square. The expected outcome for the offspring is two heterozygous offspring and two homozygous recessive. So the genotypic ratio that we expect to see is 1 to 1. That means that in the litter of 12 pups, we would expect to have six black fur pups and six white fur pups. So now we can fill out that information in the table. Next, we solve the calculation for the chi square test in order to fill out this fourth column of the table. So let's start off with the black fur calculation. First, our calculation will be open parentheses, the observed value seven minus the expected value six, close parentheses squared divided by the expected value six. And this equals 0.167. So we can fill that up, we can put that into the table. Now we repeat the process with the white fur. So our calculation is open parentheses. The observed value is five minus the expected value six, close parentheses squared divided by the expected value six. And solving for that equals 0.167 as well. Now that we have the individual trait values for the chi square calculation, we just need to add them together in order to figure out the chi square value. So our total will be 0.167 plus 0.167. So the total sum is 0.334. That means the correct answer is option C 0.334. All right, everyone. I hope you found this helpful and I'll see you soon for the next practice problem.

Verified video answer for a similar problem:

Key Concepts

Mendelian Inheritance

Chi-Square Analysis

Phenotypic Ratios