A researcher obtained a sample of 125 security analysts and asked each analyst to select four stocks on the New York Stock Exchange that were expected to outperform the Standard and Poor€™s Index over a 3- month period. One theory suggests that the securities analysts would be expected to do no better than chance. Hence, the number of correct guesses from the four ­selected stocks for any analyst would have a binomial distribution with n = 4 and Ï€ = .5 yield probabilities, as shown here:

The number of analysts€™ selections that outperformed the Standard and Poor€™s Index are given here:

Do the data support the contention that the analysts€™ performance is different from just randomly selecting four stocks?

Number Outperforming Multinomial probabilities () 0625 .25 375 25 0625 Number Outperforming Total Frequency 23 51 39 125