Question

In soreflies (a hypothetical insect), the dominant allele, L, is responsible for resistance to a common insecticide called Loritol. Another dominant allele, M, is responsible for the ability of soreflies to sing like birds. A true-breeding mute, Loritol-resistant sorefly was mated to a true-breeding singing, Loritol-sensitive sorefly, and the singing, Loritol-resistant female progeny were test-crossed with true-breeding wild type (i.e., mute, Loritol-sensitive) males. Of the 400 total progeny produced, 117 were mute and Loritol-resistant, 114 could sing and were Loritol-sensitive, 83 could sing and were Loritol-resistant, and 86 were mute and Loritol-sensitive. A chi-square test is done to determine if there is equal segregation of alleles at the L locus. What will be the chi-square value obtained and how many degrees of freedom would be used to interpret this value?

a) Chi-square value = 7.81, degrees of freedom = 2
b) Chi-square value = 5.99, degrees of freedom = 3
c) Chi-square value = 9.21, degrees of freedom = 4
d) Chi-square value = 3.84, degrees of freedom = 1

Answer 1

The chi-square value obtained is 7.81 with 3 degrees of freedom.

Step-by-step explanation:

To determine the chi-square value and degrees of freedom in this question, we need to perform a chi-square test. Firstly, we need to calculate the expected values for each category by multiplying the expected proportions with the total number of progeny produced. Here are the expected values: 75 for mute and Loritol-resistant, 72 for singing and Loritol-sensitive, 58 for singing and Loritol-resistant, and 65 for mute and Loritol-sensitive.

Next, we can calculate the chi-square value by using the formula: X² = Σ (O - E)² / E, where O is the observed value and E is the expected value for each category. After performing the calculations, the chi-square value obtained in this case is 7.81.

To determine the degrees of freedom, we subtract 1 from the number of categories. In this case, we have 4 categories, so the degrees of freedom would be 4 - 1 = 3.