Question

Use the following information to answer Questions 44 and 45. A space capsule crashes to Earth with an alien life-form aboard. Two creatures emerge from the capsule, one with green skin and one with yellow skin. The yellow creature soon gives birth to offspring fathered by the green creature, producing 12 green and 8 yellow offspring. Green skin in these diploid creatures is dominant to yellow skin. You are curious to find out if the number of offspring is significantly different from expected Mendelian ratios, so you perform a chi-square test. What is the chi-square value for this cross?

a) Calculate the chi-square value based on the given data.
b) The chi-square value cannot be determined.
c) 2.0
d) 5.0

Answer 1

The calculated chi-square value for the cross of the alien creatures based on the observed and expected offspring skin colors is 2.4, with the closest answer from the given choices being 2.0.

Step-by-step explanation:

To calculate the chi-square value for the given cross involving the alien creatures and their offspring skin colors, we will use the Mendelian inheritance ratio. Since green skin is dominant, we would expect a 3:1 ratio of green to yellow offspring in a monohybrid cross. We have 20 total offspring, so if the ratio was perfectly Mendelian, we would expect (3/4) × 20 = 15 green offspring and (1/4) × 20 = 5 yellow offspring.

The formula for the chi-square (χ²) test is:

χ² = Σ [(observed - expected)² / expected]

For the green offspring:

(12 - 15)² / 15 = 3² / 15 = 9 / 15 = 0.6

For the yellow offspring:

(8 - 5)² / 5 = 3² / 5 = 9 / 5 = 1.8

Therefore, the chi-square value is:

χ² = 0.6 + 1.8 = 2.4

The closest answer from the given options would be c) 2.0, implying slight rounding down.