Question 1171145: Assume you are the owner of a highly-respected law firm. The data below shows the number of cases won each month by two lawyers who work for you.
Lawyer A 42 61 48 54 50 49
Lawyer B 51 23 82 44 79 25
On average, would you say that these lawyers are performing equally? Why or why not? If you are looking for a lawyer with a reliable number of wins, which lawyer would you choose?
What statistic did you use to come to that conclusion? Back up your decision with statistical evidence. Do NOT just use the mean or median to explain your answer.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Looking at the data, I suspect the means are similar but the variability is much less in A than for B. The range is only 19 cases for A and 59 cases for B. Then one could use a better measure of variability like the sd.
The means are not only similar but equal.
The std dev for A is 6.38 cases and for B 25.51 cases. This is a large difference.
Means can be the same but the two samples widely different, and here they are. Statistically, were one not careful, a 2-sample t-test would show no difference, but the two sample t-test assumes that the variances of both of the samples are equal, and they are definitely not equal.
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