Mark Pollard, financial consultant for Merrill Lynch, Pierce, Fenner & Smith, Inc., is quoted in national advertisements for Merrill Lynch as saying: "I've made more money for clients by saying no than by saying yes." Suppose that Pollard allowed you access to his files so that you could conduct a statistical test of the correctness of his statement.
Suppose further that you gathered a random sample of 25 clients to whom Pollard said yes when presented with their investment proposals, and you found that the clients' average gain on investments was 12% and the standard deviation was 2.5%.
Suppose you gathered another sample of 25 clients to whom Pollard said no when asked about possible investments; the clients were then offered other investments, which they consequently made.
For this sample, you found that the average return was 13.5% and the standard deviation was 1%. Test Pollard's claim at α = 0.05. What assumptions are you making in this problem?