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Question 781:



No answer provided yet.For finding the right sample sizes it depends on whether you want to compare two or more groups to see if there is a difference, or if you want to sample a population to obtain as precise as estimate as possible. In short: comparison and precision. Your question appears to deal with the latter. You want to know how many you need to sample in order to find a sample mean of 50.

For precision, your sample size depends on three things
1. The standard deviation (which you provide as 50).
2. The level of confidence you need. This isn't stated so we'll assume it's 95%.
3. The amount of precision. This also isn't stated so we'll start with a round number like 10%.

So the question now is, how large of a sample size do you need to be within +/- 10% of your target mean or +/- 5. To do this we work backwards from the formula of a confidence interval using these steps.
  1. Divide the desired margin of error by the critical value for 95% (which is 1.96) = 5/1.96 = 2.551067
  2. Divide the standard deviation by the results from step 1 = 15/2.551067 = 5.87989
  3. Square the results from step 2 = 34.57.
We round up to get a sample size of 35 will generate a margin of error around a mean of +/-10% assuming a mean of 50 and standard deviation of 15. You can change the values to a more precise margin of error, say 5% and we get n =139 sample size.

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