Question

Conception about hypothesis test:

Q1. my professor said if the null hypothesis is true, then it is normal distribution but what does that mean? because sometimes we will reject the H0, does that mean if we reject it then it is not normal distribution?

Q2. sometimes we will have H0: u=30 something like that, but I don't understand as i was told that we don't know the population value; however u is the population value so i am confused. Plus, my professor said we need to use u to guess the true population value but why we assume u=30???

Here is my understanding: actually 30 may or may not be the true value but we assume it is true so we can do the hypothesis test???

Answer 1

1)

null hypothesis: distribution is normal

alternate hypothesis: distribution is not normal

so, yes, if we reject the Ho, then it means that distribution is not normal.

if we fail to reject Ho then we conclude that distribution is normal

2)

your concept is clear here, we just assume as in your example that true value ,u=30 is true

and in alternate hypothesis we take whether u >30 , u < 30 or u╪30.

Then we do hypothesis testing, to check which hypothesis to reject , and which to retain

based on that we make conclusions