Suppose you receive an e-mail from a stock broker who claims to be able to accurately predict whether any given stock will rise or fall in price during the subsequent month. To “prove” her claim, she makes a prediction about performance (higher price or lower price) for ten stocks over the next month. You are skeptical of the broker’s claim, and assume she simply guesses which stocks will improve or worsen in price over any given month. Put another way, you assume she has a 50% chance of being correct in her prediction for any given stock. Based on this assumption, you derive the following probabilities concerning her ten picks:
Number of correct picks
0
1
2
3
4
5
6
7
8
9
10
Probability
0.001
0.01
0.044
0.117
0.205
0.246
0.205
0.117
0.044
0.01
0.001
What is the empirically testable conclusion resulting from your deductive reasoning?
How could you test your empirically testable conclusion using a data sample?
Outline the inductive and deductive reasoning you could use to evaluate whether or not the broker is simply guessing in her stock picks.