Question 1163622: 5.An educational startup that helps MBA aspirants write their essays is targeting individuals who have taken GMAT in 2012 and have expressed interest in applying to FT top 20 b-schools. There are 40000 such individuals with an average GMAT score of 720 and a standard deviation of 120. The scores are distributed between 650 and 790 with a very long and thin tail towards the higher end resulting in substantial skewness. Which of the following is likely to be true for randomly chosen samples of aspirants?
A.The standard deviation of the scores within any sample will be 120.
B.The standard deviation of the mean of across several samples will be 120.
C.The mean score in any sample will be 720.
D.The average of the mean across several samples will be 720.
E.The standard deviation of the mean across several samples will be 0.60
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website!
The SEM is sd/sqrt(n)=120/sqrt(40000)=0.6
A. SD will not be 120 of scores in any one sample, especially since we don't know the sample size.
B. SD of mean across several samples will also not be 120. It will be less; indeed, probably about 0.6
C. The mean score in any sample will be 720. Maybe, but no reason it couldn't be less or more.
D. The average of the mean across several samples will be 720. This is certainly possible, but it requires the mean of all samples that sample size, which would be the case
E. The SEM will be 0.60. This is likely, given the sample size, which even with a lot of skewness will tend towards normality given the sample size. I would use this in calculations. The mean would have an expected value of 720, but in calculations, the SEM is 0.6.
E.
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