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

[kieranf144]

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?

 

[Jameson]

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.

 

[kieranf144]

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?

 

[pickslides]

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

$H_0: \mu_s = \mu_0$