Question

with a level of significance .05, how are yhe boundaries for the critical region determined?

Answer 1

With the level of significance,we have the condition that:

if ,then under H0,

,where w is the critical region.

Here,most of our test is based on the test statistics whose distribution under H0 is completely known.

Take for example,x1,x2,....,xn~N(,1)

To test;H0: VS H1:

Our test statistics is then T=.

Note that,T~N(0,1),under H0,a distribuution completely known and symmetric.

Hence,our {},where c is such that,

Hence,c is such that,if Z~N(0,1),P[|Z|>c]=0.05

Hence,c=