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3#
发表于 2011-7-13 15:38
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H M Walrus is exactly right. I am adding more in an attempt to elaborate it further.
1. First lets understand that if you know Mean and SD of any variable, and you know it has a normal distribution, you can graphically define the shape of its bell.
2. Next, you can define the shape of distribution of Sample Means for samples of a given fixed size, if you know the Population Mean and Population Standard Deviation. (This is from Central Limit Theorem, right?). With SD of such distribution as = Pop SD / Sqrt of sample size.
3. This distribution you thus obtained means, that, if you collect any sample of that fixed size from your population, Mean of that sample will lie within that Bell you have defined.
4. Now, to answer your question: “you mean to say that from just one sample drawn (with sample size = 30) if i calculate the mean of that sample, i can assume that, that mean will be the Population mean as well?”.
You can assume that, but you also have to know that your Sample Mean may not be exactly equal to the Population Mean. Your Sample Mean could lie anywhere within the distribution curve you plotted in step 2. This is why, it is suggested to have a large sample size. Because, larger the sample size, lower will be SD of the Sample Distribution, thinner will be your distribution Bell and closer will be your Sample mean to your actual Population Mean.
5. But larger sample size means, more research costs in terms of time and effort. So, there is a trade off between accuracy and costs.
6. So, you see, you need only 1 sample to ESTIMATE your Population Mean, but that sample should be as large as that can be afforded and should represent the Population as CLOSE as possible. That is why it is very important to understand and eliminate various Sample Biases that can get in, in your sample collection process.
Hope this helps. If you have queries we can discuss further. |
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