In fruit flies, eyes can be either white or red, and wings can be either long or short. A mating cross between a red-eyed long-winged female and a red-eyed short-winged male produces the following offpsring:



42 red, short

30 red, long

14 white, short

10 white, long


Calculate the chi-squared value for the null hypothesis that the red-eyed long-winged female was heterozygous for the long-wing gene. Express your answer as a decimal rounded the nearest hundredth.

To calculate the chi-squared value for this problem, you first need to determine the expected values for each phenotype combination under the assumption of independence.

Assuming Mendelian inheritance, we can use the Punnett square to determine the expected frequencies for each phenotype.

Let's start by determining the expected values for each phenotype combination:

Expected red, short = (total red offspring) * (total short-winged offspring) / (total offspring)
Expected red, short = (42 + 30) * (42 + 14) / (42 + 30 + 14 + 10) = 72 * 56 / 96 = 42

Expected red, long = (total red offspring) * (total long-winged offspring) / (total offspring)
Expected red, long = (42 + 30) * (30 + 10) / (42 + 30 + 14 + 10) = 72 * 40 / 96 = 30

Expected white, short = (total white offspring) * (total short-winged offspring) / (total offspring)
Expected white, short = (14 + 10) * (42 + 14) / (42 + 30 + 14 + 10) = 24 * 56 / 96 = 14

Expected white, long = (total white offspring) * (total long-winged offspring) / (total offspring)
Expected white, long = (14 + 10) * (30 + 10) / (42 + 30 + 14 + 10) = 24 * 40 / 96 = 10

Now that we have the expected values, we can calculate the chi-squared value using the formula:

Chi-squared = Σ[(observed - expected)^2 / expected]

Let's calculate it step by step:

For the red, short combination:
(observed - expected)^2 / expected = (42 - 42)^2 / 42 = 0

For the red, long combination:
(observed - expected)^2 / expected = (30 - 30)^2 / 30 = 0

For the white, short combination:
(observed - expected)^2 / expected = (14 - 14)^2 / 14 = 0

For the white, long combination:
(observed - expected)^2 / expected = (10 - 10)^2 / 10 = 0

Summing up all these values, we get:

Chi-squared = 0 + 0 + 0 + 0 = 0

Therefore, the chi-squared value for the null hypothesis is 0.