HELLO ALL. ALL MY DOUBTS ARE IN PART-4 QUESTIONS. IN QUESTION 4.3, 1(b) HOW DO WE KNOW THAT WE HAVE TO LOOK UP P(Z<-2.108)?? WHY NOT P(Z>-2.108)?? IN THE SAME QUESTION, IN (2), HOW DID THEY LOOK UP CHI-SQUARE-9 FOR THE TEST STATISTIC 12.45? THEY'VE SAID THE CRITICAL VALUES ARE 2.700 AND 19.02. HOW?? IN QUESTION 4.8, IN (1) HOW IS ALPHA=1% ? GENERALLY IF ITS NOT GIVEN, WE ASSUME ITS 5% RIGHT?? THE SAME DOUBT IN QUESTION 4.19. WHY IS ALPHA=1% WHEN ITS NOT GIVEN??? AND SAME DOUBT IN QUESTION 4.20 FOR ALPHA BEING =1.2% ?? IN (2), AGAIN WHY DO WE LOOK AT P(Z>0.45)?? WHY NOT LESS THAN?? HOW DO WE KNOW?
With a 1 sided test we simply calculate the probability in the direction given in the alternate hypothesis. For a 2 sided test the p-value is double the probability of obtaining a more extreme result - for a negative Z value the less than side is more extreme whereas for a positive Z value the greater than side is more extreme. Again it's a two-sided test at the 5% level - so the critical values are the 2½% values - so the total rejection region is 5%. The true value of alpha is the probability value. In this solution they just used 1% to say it's "highly significant" (5% is "significant") and left it at that. Since the p-value was actually 0.001%, alpha was actually 0.001%. Same thing here. The question tells us to test for a reduction. So if p2 < p1 then (p1 - p2) > 0 hence the rejection region is the "greater than" side.
