Otema Chi has a spreadsheet with 108 monthly returns for shares in Marunou Corporation. He writes a software program that uses bootstrap resampling to create 200 resamples of this Marunou data by sampling with replacement. Each resample has 108 data points. Chi’s program calculates the mean of each of the 200 resamples, and then it calculates that the mean of these 200 resample means is 0.0261. The program subtracts 0.0261 from each of the 200 resample means, squares each of these 200 differences, and adds the squared differences together. The result is 0.835. The program then calculates an estimate of the standard error of the sample mean.The estimated standard error of the sample mean is closest to:A.0.0115B.0.0648C.0.0883
Question
Otema Chi has a spreadsheet with 108 monthly returns for shares in Marunou Corporation. He writes a software program that uses bootstrap resampling to create 200 resamples of this Marunou data by sampling with replacement. Each resample has 108 data points. Chi’s program calculates the mean of each of the 200 resamples, and then it calculates that the mean of these 200 resample means is 0.0261. The program subtracts 0.0261 from each of the 200 resample means, squares each of these 200 differences, and adds the squared differences together. The result is 0.835. The program then calculates an estimate of the standard error of the sample mean.The estimated standard error of the sample mean is closest to:A.0.0115B.0.0648C.0.0883
Solution
The standard error of the sample mean is calculated by taking the square root of the variance of the sample means. In this case, the variance is given by the sum of the squared differences divided by the number of samples minus 1.
Here are the steps to calculate it:
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Calculate the variance: The sum of the squared differences is 0.835. Since there are 200 resamples, the variance is 0.835 / (200 - 1) = 0.0042.
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Calculate the standard error: The standard error is the square root of the variance. So, the standard error is sqrt(0.0042) = 0.0648.
So, the estimated standard error of the sample mean is closest to 0.0648 (Option B).
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