I'm estimating the perception threshold for stimulus intensity, the current information is available
population size or sample size n < 30, the sample mean, the collected data is normally distributed. I would like to find the probability (p-value) of getting this value (the perception threshold) by chance. because of the small sample size, I can not do a Z-test.
Therefore, I would like to do a two-tailed one-sample T-test. in order to calculate the statistical t-value, we need to know the hypothesized population mean "μo". In my case, I just estimated this value (it is the sample mean). How can I find the statistical t-value to calculate the p-value.?
Thank you very much in advance
Check if this link helps you:
https://www.dummies.com/education/math/statistics/how-to-use-the-t-test-to-handle-small-samples-and-unknown-standard-deviations/
Hello Nassr,
If your goal is to estimate a mean value based on your sample data, an ordinary confidence interval (with critical value taken from the t distribution that is appropriate for your sample df and chosen risk of CI missing the true value altogether) would do the job quite nicely.
CI = Sample mean +/- tcritical * SD / sqrt(N)
Any rival value for the population mean may therefore be evaluated as plausible or implausible, by determining whether it falls within or outside of the bounds of the confidence interval you derive.
Good luck with your work!
I'm not sure how you know the data are normal, or whether the pop n or sample n is 30, but the answer is really easy. The probability is zero. Given your variable is normal, and therefore continuous, the probability that the mean is any value is zero. I think David Morse is providing an answer to what he thinks you might be meaning, but from your question the answer is 0. If you mean something other than what you have written you might submit a new question. But, one of these answers might be enough for your needs.
Daniel Wright: Thank you very much for your replay, I have the calculate the kurtosis (0.9) if the value between -2 and 2, the dataset can be considered as normally distributed.
The stimulus intensity that I have estimated during the experiment. is never been estimated before. therefore I don't have a previous reference to compare with. Therefore, I was looking for a way to check what is the possibility to get this value by chance.
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