3 Two investment advisers make predictions about cetain stoc

3. Two investment advisers make predictions about cetain stocks. For each stock they predict whether its price will increase or decrease the following week. Their predictions are then marked as correct or incorrect. The results are summarised in the following table: Test the hypothesis that the two advisors have an equal probability of predicting correctly, at the 5% significance level.

Solution

H0: Two advisors have equal prob of predicting correctly

Ha: They do not have equal prob.

Two sided test

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Alpha = 5%

We can do chi square test for this

?² = 356.853,     df = 1,     ?²/df = 356.85 ,         P(?² > 356.853) = 0.0000

expected values are displayed in italics
individual ?²values are displayed in (parentheses)

As p value =0.00 < alpha

we reject null hypothesis.
There is significan tdifference between the two

	Comparison of investmenet advisors
Adv I correct	Adv I incorrect
Adv II correct	1021 773.34 ( 79.32)	486 733.66 ( 83.60)	1507
Adv II incorrect	402 649.66 ( 94.41)	864 616.34 ( 99.52)	1266
	1423	1350	2773