How do distributions provide a link between probabilities an

How do distributions provide a link between probabilities and statistical tests?

Solution

The statistical tests we are familiar with,almost every 1 is arising from a normal distribution and those who don\'t have normality,also in a approximate sense uses normality assumptions!
Now, from normal distribution you can achieve many distributions by some applications!

In the tests, the test statistic we are using...is so choosen that it follows some prob. distributions..
like when we know the popltn s.d..we can standardize them
and thus we are using the normal distrbtn for the tets stat..

when it is unknown...we have to estimate it from sample s.d...

then there comes t-distribution..because, the distribution of sample s.d involves the chi-square distribution by definition of chi-square. distribution and thus (normal/ chi-sq) giving introduction to a t -distbn...

similary for 2 sample s.d\'s...we have 2 chi-square distributions..and from definition..(chi-sq/ chi-sq_ is F-distribution and thus such distributional forms arises ,just in our way of standardizing...
you can refer to the deftn of chi-sq,t and F distrn and seeing how they are arising from the normal distribution, you will be able to understand this!