Tim is a stock market trader. One day he invents a trading

strategy that he believes will make money on any given trading day. Suppose

he wants to test the null hypothesis that his trading strategy has the same

chance of making money as that of a fair coin toss, against the alternative

hypothesis that his trading strategy has a higher chance of making money

than that of a fair coin toss.

Suppose Tim comes up with the following decision rule: If his

trading strategy can make money on 5 or more trading days out of 6

randomly selected and independent trading days, then he will reject the

null hypothesis in part

(a). Calculate the probability of committing a type

I error when his trading strategy is in fact the same as a fair coin toss.

(b) Calculate the probability of rejecting the null hypothesis based

on Tim's decision rule when his trading strategy actually has a

75% chance of making money on any .trading day. Does your answer make

sense to you? Explain.