Speculate
Subject:StatisticsPrice:4.87 Bought7
Speculate.com is an internet trading company. The company is worried about the continual market slide; it seems to have resulted in a significant decline in both the total number of trades Speculate.com and the number of customers who actively trade on Speculate.com .
1.According to the results of a recent survey among 150 randomly selected Speculate.com customers, the average return on $1 invested among the 150 respondents was 96 cents (they lost 4 cents) with a sample variance of (25 cents) Based on the survey results, how confident can you be that Speculate.com customers are losing money on average?
2. A Speculate.com customer is considered “active” if s/he executes at least one trade per day. September 2003 records indicate that 20% of customers were “active” and that one-quarter of “active” customers outperformed S&P 500 index during that period. On the other hand, one-third of the “nonactive” customers outperformed S&P 500 index during that period. What percentage of customers who outperformed S&P 500 index in September 2003 were “active” customers in that month?
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Answer:
1) Very confident
2) Roughly 15.8%
Step-by-step explanation
1) The sampling distribution has mean 96 cents and standard deviation 5/sqrt(150) = 0.4082 cents. Thus breaking even, or 100, has a z score of (100-96)/0.4082 = -9.80, which is overwhelming evidence that the average user is losing money.
2) 20% are active and 1/4 of those outperform, or 5% total. 80% are inactive and 1/3 outperform, or 26.67%. Thus a total of 31.67% outpeform, and active traders are 5/31.67 or ~15.8% of those.
