【正文】 0 . 6 7 4 1 . 2 8 2 1 . 6 4 5 1 . 9 6 2 . 3 2 6 2 . 5 7 6 3 . 2 9 1A r e a u n d e r t h e c u r v ed f , ut ( a, u ) a Area under the curve Abcot Percentiles of the Normal Distribution / Z Distribution 0 0 . 0 1 0 . 0 2 0 . 0 3 0 . 0 4 0 . 0 5 0 . 0 6 0 . 0 7 0 . 0 8 0 . 0 90 0 . 5 0 0 0 0 . 5 0 4 0 0 . 5 0 8 0 0 . 5 1 2 0 0 . 5 1 6 0 0 . 5 1 9 9 0 . 5 2 3 9 0 . 5 2 7 9 0 . 5 3 1 9 0 . 5 3 5 90 . 1 0 . 5 3 9 8 0 . 5 4 3 8 0 . 5 4 7 8 0 . 5 5 1 7 0 . 5 5 5 7 0 . 5 5 9 6 0 . 5 6 3 6 0 . 5 6 7 5 0 . 5 7 1 4 0 . 5 7 5 30 . 2 0 . 5 7 9 3 0 . 5 8 3 2 0 . 5 8 7 1 0 . 5 9 1 0 0 . 5 9 4 8 0 . 5 9 8 7 0 . 6 0 2 6 0 . 6 0 6 4 0 . 6 1 0 3 0 . 6 1 4 10 . 3 0 . 6 1 7 9 0 . 6 2 1 7 0 . 6 2 5 5 0 . 6 2 9 3 0 . 6 3 3 1 0 . 6 3 6 8 0 . 6 4 0 6 0 . 6 4 4 3 0 . 6 4 8 0 0 . 6 5 1 70 . 4 0 . 6 5 5 4 0 . 6 5 9 1 0 . 6 6 2 8 0 . 6 6 6 4 0 . 6 7 0 0 0 . 6 7 3 6 0 . 6 7 7 2 0 . 6 8 0 8 0 . 6 8 4 4 0 . 6 8 7 90 . 5 0 . 6 9 1 5 0 . 6 9 5 0 0 . 6 9 8 5 0 . 7 0 1 9 0 . 7 0 5 4 0 . 7 0 8 8 0 . 7 1 2 3 0 . 7 1 5 7 0 . 7 1 9 0 0 . 7 2 2 40 . 6 0 . 7 2 5 7 0 . 7 2 9 1 0 . 7 3 2 4 0 . 7 3 5 7 0 . 7 3 8 9 0 . 7 4 2 2 0 . 7 4 5 4 0 . 7 4 8 6 0 . 7 5 1 7 0 . 7 5 4 90 . 7 0 . 7 5 8 0 0 . 7 6 1 1 0 . 7 6 4 2 0 . 7 6 7 3 0 . 7 7 0 4 0 . 7 7 3 4 0 . 7 7 6 4 0 . 7 7 9 4 0 . 7 8 2 3 0 . 7 8 5 20 . 8 0 . 7 8 8 1 0 . 7 9 1 0 0 . 7 9 3 9 0 . 7 9 6 7 0 . 7 9 9 5 0 . 8 0 2 3 0 . 8 0 5 1 0 . 8 0 7 8 0 . 8 1 0 6 0 . 8 1 3 30 . 9 0 . 8 1 5 9 0 . 8 1 8 6 0 . 8 2 1 2 0 . 8 2 3 8 0 . 8 2 6 4 0 . 8 2 8 9 0 . 8 3 1 5 0 . 8 3 4 0 0 . 8 3 6 5 0 . 8 3 8 91 0 . 8 4 1 3 0 . 8 4 3 8 0 . 8 4 6 1 0 . 8 4 8 5 0 . 8 5 0 8 0 . 8 5 3 1 0 . 8 5 5 4 0 . 8 5 7 7 0 . 8 5 9 9 0 . 8 6 2 11 . 1 0 . 8 6 4 3 0 . 8 6 6 5 0 . 8 6 8 6 0 . 8 7 0 8 0 . 8 7 2 9 0 . 8 7 4 9 0 . 8 7 7 0 0 . 8 7 9 0 0 . 8 8 1 0 0 . 8 8 3 01 . 2 0 . 8 8 4 9 0 . 8 8 6 9 0 . 8 8 8 8 0 . 8 9 0 7 0 . 8 9 2 5 0 . 8 9 4 4 0 . 8 9 6 2 0 . 8 9 8 0 0 . 8 9 9 7 0 . 9 0 1 51 . 3 0 . 9 0 3 2 0 . 9 0 4 9 0 . 9 0 6 6 0 . 9 0 8 2 0 . 9 0 9 9 0 . 9 1 1 5 0 . 9 1 3 1 0 . 9 1 4 7 0 . 9 1 6 2 0 . 9 1 7 71 . 4 0 . 9 1 9 2 0 . 9 2 0 7 0 . 9 2 2 2 0 . 9 2 3 6 0 . 9 2 5 1 0 . 9 2 6 5 0 . 9 2 7 9 0 . 9 2 9 2 0 . 9 3 0 6 0 . 9 3 1 91 . 5 0 . 9 3 3 2 0 . 9 3 4 5 0 . 9 3 5 7 0 . 9 3 7 0 0 . 9 3 8 2 0 . 9 3 9 4 0 . 9 4 0 6 0 . 9 4 1 8 0 . 9 4 2 9 0 . 9 4 4 11 . 6 0 . 9 4 5 2 0 . 9 4 6 3 0 . 9 4 7 4 0 . 9 4 8 4 0 . 9 4 9 5 0 . 9 5 0 5 0 . 9 5 1 5 0 . 9 5 2 5 0 . 9 5 3 5 0 . 9 5 4 51 . 7 0 . 9 5 5 4 0 . 9 5 6 4 0 . 9 5 7 3 0 . 9 5 8 2 0 . 9 5 9 1 0 . 9 5 9 9 0 . 9 6 0 8 0 . 9 6 1 6 0 . 9 6 2 5 0 . 9 6 3 31 . 8 0 . 9 6 4 1 0 . 9 6 4 9 0 . 9 6 5 6 0 . 9 6 6 4 0 . 9 6 7 1 0 . 9 6 7 8 0 . 9 6 8 6 0 . 9 6 9 3 0 . 9 6 9 9 0 . 9 7 0 61 . 9 0 . 9 7 1 3 0 . 9 7 1 9 0 . 9 7 2 6 0 . 9 7 3 2 0 . 9 7 3 8 0 . 9 7 4 4 0 . 9 7 5 0 0 . 9 7 5 6 0 . 9 7 6 1 0 . 9 7 6 72 0 . 9 7 7 2 0 . 9 7 7 8 0 . 9 7 8 3 0 . 9 7 8 8 0 . 9 7 9 3 0 . 9 7 9 8 0 . 9 8 0 3 0 . 9 8 0 8 0 . 9 8 1 2 0 . 9 8 1 72 . 1 0 . 9 8 2 1 0 . 9 8 2 6 0 . 9 8 3 0 0 . 9 8 3 4 0 . 9 8 3 8 0 . 9 8 4 2 0 . 9 8 4 6 0 . 9 8 5 0 0 . 9 8 5 4 0 . 9 8 5 72 . 2 0 . 9 8 6 1 0 . 9 8 6 4 0 . 9 8 6 8 0 . 9 8 7 1 0 . 9 8 7 5 0 . 9 8 7 8 0 . 9 8 8 1 0 . 9 8 8 4 0 . 9 8 8 7 0 . 9 8 9 02 . 3 0 . 9 8 9 3 0 . 9 8 9 6 0 . 9 8 9 8 0 . 9 9 0 1 0 . 9 9 0 4 0 . 9 9 0 6 0 . 9 9 0 9 0 . 9 9 1 1 0 . 9 9 1 3 0 . 9 9 1 62 . 4 0 . 9 9 1 8 0 . 9 9 2 0 0 . 9 9 2 2 0 . 9 9 2 5 0 . 9 9 2 7 0 . 9 9 2 9 0 . 9 9 3 1 0 . 9 9 3 2 0 . 9 9 3 4 0 . 9 9 3 62 . 5 0 . 9 9 3 8 0 . 9 9 4 0 0 . 9 9 4 1 0 . 9 9 4 3 0 . 9 9 4 5 0 . 9 9 4 6 0 . 9 9 4 8 0 . 9 9 4 9 0 . 9 9 5 1 0 . 9 9 5 22 . 6 0 . 9 9 5 3 0 . 9 9 5 5 0 . 9 9 5 6 0 . 9 9 5 7 0 . 9 9 5 9 0 . 9 9 6 0 0 . 9 9 6 1 0 . 9 9 6 2 0 . 9 9 6 3 0 . 9 9 6 42 . 7 0 . 9 9 6 5 0 . 9 9 6 6 0 . 9 9 6 7 0 . 9 9 6 8 0 . 9 9 6 9 0 . 9 9 7 0 0 . 9 9 7 1 0 . 9 9 7 2 0 . 9 9 7 3 0 . 9 9 7 42 . 8 0 . 9 9 7 4 0 . 9 9 7 5 0 . 9 9 7 6 0 . 9 9 7 7 0 . 9 9 7 7 0 . 9 9 7 8 0 . 9 9 7 9 0 . 9 9 7 9 0 . 9 9 8 0 0 . 9 9 8 12 . 9 0 . 9 9 8 1 0 . 9 9 8 2 0 . 9 9 8 2 0 . 9 9 8 3 0 . 9 9 8 4 0 . 9 9 8 4 0 . 9 9 8 5 0 . 9 9 8 5 0 . 9 9 8 6 0 . 9 9 8 63 0 . 9 9 8 7 0 . 9 9 8 7 0 . 9 9 8 7 0 . 9 9 8 8 0 . 9 9 8 8 0 . 9 9 8 9 0 . 9 9 8 9 0 . 9 9 8 9 0 . 9 9 9 0 0 . 9 9 9 0A r e a u n d e r t h e c u r v eZZ a Area under the curve Whereby, Shaded area = onetailed probability of occurence a = 1 – Shaded area Abcot Student t Distrbution example FDA requires pharmaceutical panies to perform extensive tests on all new drugs before they can be marketed to the public. The first phase of testing will be on animals, while the second phase will be on human on a limited basis. PWD is a pharmaceutical pany currently in the second phase of testing on a new antibiotic project. The chemists are interested to know the effect of the new antibiotic on the human blood pressure, 和 they are only allowed to test on 6 patients. The result of the increase in blood pressure of the 6 tested patients are as below: ( , , , , , ) Construct a 95% confidence interval for the average increase in blood pressure for patients taking the new antibiotic, using both normal 和 t distributions. Abcot Student t Distrbution example (con’t) Using normal or z distribution 0 . 7 6 2 . 2 8 3 ( 0 . 3 8 8 ) 1 . 9 6 2 . 2 8 3 nS Z X i n t e r v a l c o n f i d e n c e 9 5 % S De v i a t i o n , S t d 2 . 2 8 3 61 3 . 7 2 . 1 ) 2 . 7 3 . 4 0 . 8 3 ( 1 . 7 X M e a n ,0 . 0 5 l e v e l , Co n f i d e n c e6 n s i z e , S a m p l e2) / (???????????????????????aa 6Using student t distribution 0 . 9 9 7 2 . 2 8 3 ( 0 . 3 8 8) 2 . 5 7 1 2 . 2 8 3 nS t X i n t erv al c o n f i d e n