Month Year DJIA Experts Pick Dart Pick Jul 1990 2.5 12.65 0 Aug 1990 11.5 26.4 1

Question

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?

Explanation / Answer

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

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