Math Problem?

Question

There is some evidence that, in the years 1981-85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks).
Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.72%, with a standard deviation of 0.20%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years.
(a) According to Chebyshev's theorem, at least 84% of the relative increases in stock price lie between ( % ) and ( %)
round your answer 2 decimal places.

Answer 1

I have decided that I am not going to do anyones homework on Fridays. This clearly includes this problem. I recommend that you get the book and get to work on this.

The starting point is as follows:

The proportion of values from a data set that will fall within k standard deviations of the mean will be at least 1 - 1/k2, where k is any number greater than 1.

For k = 2, 75% of the values will lie within 2 standard deviations of the mean. For k = 3, approximately 89% will lie within 3 standard deviations.

Answer 2

1

Answer 3

There happens to be a subtle statistics error in this question. It is so subtle that most people, including professors are unaware it is present.

Stock prices MUST be Cauchy distributed and only from time to time appear normally distributed.

The measured mean and standard deviation is an attempt to estimate the true mean and standard deviation. However the true mean in a Cauchy distribution is undefined and the standard deviation is infinite.

Since the true standard deviation is infinite Chebyshev's Inequality cannot apply and median based statistics should be used instead.

Also, Chebyshev's formula can be found at http://en.wikipedia.org/wiki/Chebyshev%27s_inequality

And the answer is 2.5 standard deviations, which is .72+/-(2.5*.2).

This answer is however, incorrect since the inequality DOES NOT apply.