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Understanding the relationship between a 'sampling distribution of a statistic' and a 'population distribution' in the context of a 'hypothesis test'

I would like to confirm that I am understanding the relationship between a sampling distribution of a statistic (an example of a 'statistic' would be a sample mean $\bar{x}$) and a population ...
S.C.'s user avatar
  • 71
3 votes
2 answers
278 views

How to describe in words the logical conclusion of a one-tail t-test?

Lets say we have the following null and alternative hypothesis: $$H_0: \mu = \mu_0, \; H_A:\mu > \mu_0 $$ Thus, the p-value in this situation represents the probability of obtaining test results ...
Nova's user avatar
  • 719
4 votes
5 answers
2k views

Why is the concept of the Null hypothesis associated with the student's t distribution?

There are dozens of continuous probability distributions like Gaussian (normal), Variance-gamma, Holtsmark, etc. Yet, the concept of the Null hypothesis is basically associated with Student's t-...
Kernel's user avatar
  • 107
0 votes
1 answer
2k views

R: Simulation distribution: p-value and t-test

The theory suggests that P-values should follow a Uniform distribution if the null hypothesis is true. I am testing H0: mean control= mean treatment. With 2 differents simulation methods: 1)p value ...
Rodrigo_BC's user avatar
0 votes
1 answer
55 views

help interpreting t-test and p-value - or help me finding a good statistical test

I have two samples background and input these are the histograms: sample sizes are well above the 1000s, so the sample variance of the mean is pretty much low. I'm trying to have a statistic ...
Marco Pietrosanto's user avatar