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I have the following samples:

  1. System 1- Sample size = 1000 with known mean and standard deviation
  2. System 2- Sample size = 10 with known mean and standard deviation

I need to formulate a hypothesis and check if the second system has a more constant weight (meaning that the sample results are closer to the mean).

My first question is how can I compare two systems that have a big difference in the sample size (e.g. for Sys1 I will be using normal distribution but for sys2 i cannot as sample is too small, then I'd have to use T distribution and that messes up my normal comparison flow).

My second question for the hypothesis, should I base the null and alternative hypothesis based on the equality and inequality of the standard deviation? My guess is that if we base our test on the standard deviation, we can define the spread of the data around the mean and find consistency.

Any supporting documents will help.

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