Question

You are a researcher examining the expression pattern of a wobbly fly phenotype. You have flies that fly straight and those having a wobble flight. When you cross a straight flying strain with a strain showing a wobble flight, all the F1 flies fly straight. In the F2 generation, you get 762 straight flying flies and 238 wobbly flies. Your null hypothesis is that one gene controls flight patterns and that straight is dominant to wobbly. Use chi square analysis to test your hypothesis. What is your chi square number? Do you reject or fail to reject the null hypothesis?

Answer 1

After calculating the chi-square number as 0.768 and comparing it with the critical value of 3.84, we fail to reject the null hypothesis, suggesting that a single gene controls the flight pattern in fruit flies, with straight flight being dominant over wobbly flight.

Step-by-step explanation:

The student's hypothesis suggests that there is a single gene that controls flight patterns in fruit flies, where the straight flight pattern is dominant over the wobbly flight. To test this hypothesis using a chi-square analysis, the expected ratio for Mendelian inheritance of a dominant-recessive trait would be 3:1 in the F2 generation. Therefore, for a total of 1,000 flies (762 straight and 238 wobbly), the expected number of straight flying flies would be 750, and the expected number of wobbly flies would be 250.

Using the formula for chi-square (χ²) analysis, which is χ² = Σ((observed - expected)^2 / expected), we calculate:

• For straight flying flies: ((762 - 750)^2) / 750 = (144) / 750 = 0.192
• For wobbly flying flies: ((238 - 250)^2) / 250 = (144) / 250 = 0.576

Adding these two values gives us a chi-square number of 0.192 + 0.576 = 0.768.

With one degree of freedom (since there are two categories - straight or wobbly flight) and a significance level typically set at 0.05, the critical value from the chi-square distribution table is 3.84. Because 0.768 is less than 3.84, we fail to reject the null hypothesis. This means that the observed data does not significantly deviate from the expected 3:1 ratio, supporting the idea that one gene with two alleles, where straight flight is dominant, is responsible for the flight patterns in these fruit flies.