Month Year DJIA Experts Pick Dart Pick Jul 1990 25 1265 0 Au

Month	Year	DJIA	Experts Pick	Dart Pick
Jul	1990	2.5	12.65	0
Aug	1990	11.5	26.4	1.775
Sep	1990	-2.3	2.525	-14.3
Oct	1990	-9.2	-19.975	-7.225
Nov	1990	-8.5	-37.825	-16.35
Dec	1990	-12.8	-33.275	-27.45
Jan	1991	-9.3	-10.15	-22.5
Feb	1991	-0.8	-20.325	-37.3
Mar	1991	11	38.9	-2.525
Apr	1991	15.8	20.225	11.2
May	1991	16.2	50.575	72.9
Jun	1991	17.3	66.95	21.1
Jul	1991	17.7	7.5	28.675
Aug	1991	7.6	17.475	44.825
Sep	1991	4.4	39.6	71.275
Oct	1991	3.4	15.325	2.825
Nov	1991	4.4	12.4	40.975
Dec	1991	-3.3	3	-23.225
Jan	1992	6.6	12.225	4.15
Feb	1992	6.5	39.225	-14.025
Mar	1992	8.6	51.2	11.65

Problem 2- The Monkeys and Stock Market - use file \"stock.xls\" A common taunt against stock market experts is that their selection of stock portfolios is no better than stocks picked by monkeys randomly throwing darts at tables of company names. This adage was put to the test by The Wall Street Journal in 1990 when portfolios selected by experts were compared to random (darts) selections. The resulting average gains and losses on each of the Portfolios were recorded for 2 years and tabulated. Assume that each period\'s gains or losses are independent. Create a 95% hypothesis test to determine whether the gains made by the experts\' portfolios are significantly better than the gains made by the darts. What test should we use to determine this?

Solution

we should use F-test by using ANOVA. The ANOVA technique applies when there are two or more than two independent groups. The technique to test for a difference in more than two independent means is an extension of the two independent samples procedure discussed previously which applies when there are exactly two independent comparison groups.

So the hypothesis is

H₀:the means are equal

H₁: the means are not equal

By using excel we calculate the ANOVA table

The F> F-critical, So, we reject H0 that is the gains made by the expert portfolios are significantly better than the gains made by the darts.

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	27405.36	20	1370.268	3.869992	0.00164	2.096033
Within Groups	7435.578	21	354.0751
Total	34840.94	41