Question

8. Suppose there is an alien species that lays eggs. Each alien lays 6 eggs at a time. On average, 48% of the alien eggs have purple polka dots and 52% have yellow polka dots. You are offered a bet. If you find a sample in which only 20% of eggs have yellow polka dots, you win 43 space dollars. You can either take the entire colony of 1000 aliens as your sample or pick your favorite alien and use just its eggs as your sample. Which sample do you choose and why? (10 points)

Answer 1

Entire colony of 1000 aliens. Since average value is applicable only to group not individual. The given information may not hold for a individual alien. If I choose my favorite alien is one which always lays Yellow polka dot, then definitely I will lose. It is possible , since extreme values are involved in the calculation of average. So if I use entire colony as my sample then I have confidence of 68% for win.