As part of a study of environmental influences on sex determination in the fish Menidia, scientists captured every egg that a single female fish laid during a mating season in the Gulf of Mexico when waters were unseasonably warm. Of the eggs that were captured in the sample, 63% of them were female and 37% were male. Given: critical value = 3.84

a. Assuming this was a random sample with independent observations, which test would be appropriate to see if there is an even distribution of female and male fish? Write the appropriate null and alternative hypotheses.

b. If they wanted to conduct the analysis from part (a), what other information would they need? Be specific.

c. To increase the power of this hypothesis test, the scientists decided to capture the eggs of 3 other fish that season, which essentially tripled their sample size. Why would they no longer be able to run the analysis from part (a) with the new data they collected? Be specific.