Hypotheses Testing: Sample Size <10 & Known Population Mean/Std Dev

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Discussion Overview

The discussion revolves around hypothesis testing with a sample size of less than 10, specifically addressing the use of known population mean and standard deviation in the context of T tests. Participants explore the appropriate calculation of standard error in this scenario.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether to use the population or sample standard deviation for calculating standard error when the population standard deviation is known.
  • Another participant expresses curiosity about the necessity of sampling if the population mean and variance are already known.
  • A participant clarifies that they are sampling due to differences in treatment between the sample and the population, seeking to determine if these differences are significant.
  • One participant suggests using a one-sample T test with the population mean as the benchmark for comparison.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints regarding the use of standard deviation and the rationale for sampling, indicating that no consensus has been reached.

Contextual Notes

Participants have not fully resolved the implications of using population versus sample standard deviation for standard error calculation, nor have they clarified the conditions under which the sampling is justified.

kieranf144
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Hi
I'm working on something where the sample size is less than 10 and I know the population mean and standard deviation. When using the T test most of the examples I find calculate the standard error from the sample standard deviation but these are cases where the population standard deviation is unknown. Should I be using the population or sample standard deviation to calculate the standard error?
 
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Hi kieranf144,

Welcome to MHB! :)

I'm curious, if you already know the population mean and variance then why are you sampling? In any case, the standard error is calculated using the sample variance.
 
Thanks. I have a sample that has been treated differently to the population and I'm trying to see if the difference is significant. Do you think that sounds correct?
 
I would try a one sample T test and use the population mean as the benchmark.

In this case the population mean $\mu_0$ and the hypothesised mean from your sample as $\mu_s$ and

$H_0: \mu_s = \mu_0$
 

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