You are doing lab work with a new species of beetle.You isolated lines that breed true for either blue shells and long antenna, or green shells and short antenna.Crossing these lines yields F₁ progeny with blue shells and long antenna.Crossing F₁ progeny with beetles that have green shells and short antenna yield the following progeny: A chi-square test is done to test for independent assortment.What is the resulting chi-square value and how many degree(s)of freedom should be used in its interpretation? A)27.1 and one degree of freedom B)14.9 and three degrees of freedom C)14.9 and two degrees of freedom D)27.1 and three degrees of freedom E)0)42 and two degrees of freedom

Question

Quizplus · Accepted Answer

To calculate the chi-square value, we must first calculate the expected number of each phenotype based on the assumption of independent assortment. We can create a Punnett square to determine these expected numbers:

| B1   B1   b1   b1 
    ________|________________
    A1 a1  | B1A1 B1a1 b1A1 b1a1
    A1 a1  | B1A1 B1a1 b1A1 b1a1

From this Punnett square, we can see that we expect 1/4 of the progeny to have blue shells and long antennae (B1A1), 1/4 to have green shells and short antennae (b1a1), 1/4 to have blue shells and short antennae (B1a1), and 1/4 to have green shells and long antennae (b1A1).

Based on these expected numbers, we can calculate the chi-square value as:

χ2=((O1−E1)2/E1)+((O2−E2)2/E2)+((O3−E3)2/E3)+((O4−E4)2/E4)
where O represents the observed numbers (as provided in the progeny data) and E represents the expected numbers.

Using the provided progeny data, we can calculate the observed numbers as follows:

- 5 blue shells, long antennae
- 3 blue shells, short antennae
- 3 green shells, long antennae
- 5 green shells, short antennae

And we can calculate the expected numbers based on our Punnett square as follows:

- 4.5 blue shells, long antennae
- 4.5 green shells, short antennae
- 1.5 blue shells, short antennae
- 1.5 green shells, long antennae

Plugging these values into our chi-square formula, we get:

χ2=((5−4.5)2/4.5)+((3−1.5)2/1.5)+((3−4.5)2/4.5)+((5−1.5)2/1.5)≈27.1

To determine the degrees of freedom, we use the formula:

df=(number of phenotypes−1)×(number of crosses−1)=(4−1)×(2−1)=3

Therefore, the resulting chi-square value is 27.1, and we should use three degrees of freedom in its interpretation.

You Are Doing Lab Work with a New Species of Beetle.You