Question
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
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.
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