Question

2. As part of a study of environmental influences on sex determination in the fish Menidia, eggs from a single mating were divided into two groups and raised in either a warm or a cold environment. The data show that 65 of 141 offspring in the warm environment and 107 of 169 offspring in the cold environment were females.

a. Test the hypothesis that the distribution of female and male fish follows a 1:1 ratio in the cold environment. Ascertain that your assumptions are met, and then do the test. (2pts)

b. What are the odds of the fish in the cold environment being female? (1pt)

c. Calculate the odds ratio of the fish being female in the cold environment compared to the warm environment. Interpret this odds ratio in the context of the question. (1pt)

Answer 1

Environmental influences on sex in fish Menidia

	Male	Female
Warm	76	65
Cold	62	107

a) Using Minitab, our Chi square test statistic is 9.2223 and p value is 0.002 < 0.05

Hence, at 5% level of significance we can conclude that environment influences the sex in the fish Menidia. Hence we reject the hypothesis that the distribution of female and male fish follows a 1:1 ratio in the cold environment

b) odds of the fish in the cold environment being female = 107/62 = B = 1.7258

c) odds of the fish in the warm environment being female = 65/76 = C

So. odds ratio of the fish being female in the cold environment compared to the warm environment= B/C = 2.0179 = 2 (approx)

Hence, A fish is twice likely to be a female in the cold environment as compared to the warm environment