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

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SUMMARY

This discussion focuses on hypothesis testing with a sample size of less than 10, where the population mean and standard deviation are known. The consensus is that the standard error should be calculated using the sample variance, even when the population standard deviation is available. A one-sample T-test is recommended, utilizing the known population mean as the benchmark for comparison. The null hypothesis is defined as H0: μs = μ0, where μs is the sample mean and μ0 is the population mean.

PREREQUISITES
  • Understanding of T-tests and their applications
  • Knowledge of hypothesis testing concepts
  • Familiarity with standard error calculations
  • Basic statistical terminology, including population mean and variance
NEXT STEPS
  • Research the calculation of standard error using sample variance
  • Learn about one-sample T-tests and their implementation
  • Explore the implications of small sample sizes in statistical testing
  • Study the formulation and interpretation of null hypotheses in hypothesis testing
USEFUL FOR

This discussion is beneficial for statisticians, data analysts, and researchers involved in hypothesis testing, particularly those working with small sample sizes and known population parameters.

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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