standard error question
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You do not have a proper understanding. The population has a standard deviation. There is nothing you can do about it.
If we ask a better question, we might be able to make up an answer.
Given a population with unknown standard deviation and unknown mean, we are attempting to estimate the mean. A sample of 300 produced a sample mean (the we don't care about at thte moment) with a sample standard deviation of the mean of 20,000. What would be the sample standard deviation of the mean if we increased the sample size to 1,000?
\(\displaystyle 20000 = \frac{Something}{\sqrt{300}}\)
Now what?
If we ask a better question, we might be able to make up an answer.
Given a population with unknown standard deviation and unknown mean, we are attempting to estimate the mean. A sample of 300 produced a sample mean (the we don't care about at thte moment) with a sample standard deviation of the mean of 20,000. What would be the sample standard deviation of the mean if we increased the sample size to 1,000?
\(\displaystyle 20000 = \frac{Something}{\sqrt{300}}\)
Now what?
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You do not have a proper understanding. The population has a mean. There is nothing you can do about it. Why would the mean change if you picked a larger sample. Would you expet the Sample Mean to change?
\(\displaystyle 20000 = \frac{Something}{\sqrt{300}} \implies\) What?
Maybe, \(\displaystyle \frac{Something}{\sqrt{1000}} = \frac{Something}{\sqrt{1000}}\cdot\frac{\sqrt{300}}{\sqrt{300}} = \frac{Something}{\sqrt{300}}\cdot\frac{\sqrt{300}}{\sqrt{1000}} = 20000\cdot\frac{\sqrt{300}}{\sqrt{1000}}\)
Are we getting anywhere?
\(\displaystyle 20000 = \frac{Something}{\sqrt{300}} \implies\) What?
Maybe, \(\displaystyle \frac{Something}{\sqrt{1000}} = \frac{Something}{\sqrt{1000}}\cdot\frac{\sqrt{300}}{\sqrt{300}} = \frac{Something}{\sqrt{300}}\cdot\frac{\sqrt{300}}{\sqrt{1000}} = 20000\cdot\frac{\sqrt{300}}{\sqrt{1000}}\)
Are we getting anywhere?
Thank you for your help.
I appreciate that a population has an inherent mean but ...let's say that the population has 1M data points and we get a sample of this population that contains a 100 points, and a sample that contains 10,000 points. Wouldn't the larger sample have a mean that better approximates the population mean?
I appreciate that a population has an inherent mean but ...let's say that the population has 1M data points and we get a sample of this population that contains a 100 points, and a sample that contains 10,000 points. Wouldn't the larger sample have a mean that better approximates the population mean?
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The expected value of an unbiased estimator of the mean is the mean of the underlying distribution. The sample mean will change with a different sample, whether smaller or larger, but this is only a function of the sample. If you take another sample of the same size, you will get a different sample mean (unless something weird happens). There is nothing about a sample size that says "This is the real mean of the population", well, until your sample is the entire population, but that's not really a sample, is it? The goal of a larger sample size is the decrease in the variance.