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

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When conducting hypothesis testing with a sample size of less than 10 and known population mean and standard deviation, the standard error should be calculated using the sample variance. Despite knowing the population parameters, sampling may still be necessary to assess differences due to treatment variations. A one-sample T test is appropriate, using the population mean as the benchmark for comparison. The null hypothesis can be stated as H0: μs = μ0, where μs is the sample mean and μ0 is the population mean. This approach allows for evaluating the significance of the observed differences.
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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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