Question 369083
 <pre><font size = 3 color = "indigo"><b>
Hi,
The critical regions appropriate to be used to test the null hypothesis will
depend on the parameters set by Ho & Ha.  In general:
	a	a/2	crtical regions	
90%	10	5%	z <-1.645	z >+1.645
95%	5	2.50%	z <-1.96	z >+1.96
98%	2	1%	z <-2.33	z >+2.33
99%	2	0.50%	z<-2.575	z >+2.575
For example when testing the Ho, the following would be used and will result
in a negative or positive number depending on the value of X used in the
test statistic = {{{(X - mu)/(sigma/sqrt(n))}}}	

(A) Ho: u &#8805; 81 and Ha: u <81, a = 0.05
this will result in a negative test statistic as the test value used for X < u
therefore, the critical region would be z < -1.96

(B) Ho: u= 45 and Ha: u<45 or>45, a = 0.10
The result for a test statistic here may be neg or positive depending on test value of X used
therefore, the critical regions would be z< -1.645 or z > +1.64

(C)Ho: u &#8804; 88, a = 0.01
The result for this test statistic will be positve because test value used for X > u
therefore, the critical regions would be  z > +2.33
Hope this helps to clear this up.