Question

The Methodical Pharmaceutical Company is trying to a new product that is supposed to detect a certain substance that is banned in athletic competition. Among 83 subjects with positive tests results there were 6 false positives (indicating that they had used the banned substance when they in fact had not); among 57 subjects with negative tests results, there were 2 false negative results (indicating they had not used the banned substance when in fact they had). How many subjects are included in this study? a. b. How many of the subject had a true negative result? What is the probability, rounded to four decimal places, that a randomly selected subject had a true negative result? C. If one of the subjects is selected at random, find the probability (rounded to four decimal places) that the subject tested positive or did not use the banned substance. 2. 14 Find the positive predictive value for the test; that is, find the probability (rounded to four decimal places) that a subject has used the banned substance, given the subject tested positive. Is the probability high enough (that is, over 95%) to make the test appear to be effective? Probability Effective or Not Effective

Answer 1

83 positive test esula L balpe po fiheve ie, thay cua actualy achive negativef truy they ShoulA get negahve rerut) 6- 83 ads positve Stmilauy 53 negakve tegt rerult L 2 talpe negahive iey thay Lactually posive are 55-m negahiva ts posikva 2.- (a)Tobol subjecty 83t57 40 (b) 54 got negative regult, cumsng them 2 negatise false negative auze true 55 Number o true neg ahve Total subjecs e)Probabiity 55 O 3929 mactrsse 11 (2). A-tes bed posihive did not uee tte oanned &beon B n (AUB) Y A) + mEB) - LANB) L bes ted posihive and dit & not Lup e banned suts bance 83 + / 77+ 2) 85 85 n(AUB) Total subjety

Auged the banned subgbone 3 ested posih ve PLANB PCA/B)= PCB) pobability 83 A gwen B 0.9277 = 92.47%0 Not oechve