Chy Coliege of Ne Department of Mat hematics MATH 3owoo Problem(8)(10 pts.] Supp

Question

Chy Coliege of Ne Department of Mat hematics MATH 3owoo Problem(8)(10 pts.] Suppose in a survey, 400 asthmatics were chosen to study the effects of a new anti- asthmatic drug. In 2x 3 contingency table below, each patient is classified according to (i) his or her prior allergic history with anti-aesthmaticslrow categories) and (ii) the effect of the new medication on the patient(Column categories) Improvement() No change (N) |Allergic reaction(AR) ROW Totals Allergic history (A) 30 30 120 Not allergic (Ae) 400 Column Totals 280 40 (a)Fill the missing entries in the table. (b) Based on the data, what is the probability that a randomly chosen asthmatic will experience an improvement with the new drug. (c) What is the probability that an asthmatic with history of allergies will have im- provement? Express the answer as a conditional probability. (d) Based on data, would you say that events A and I are independent? Justify your answer and explain its medical significance.

Explanation / Answer

a)

b) probablity thata randomly choosen asthamatic will experience improvement= 280/400=7/20

c) Probability that an asthmatic with history of allergies will have improvment=(60/120)=1/2

d) they both are independent as Improvement is constant even as the no. of Allergic history count changes.

Improvement No chnage Allergic reaction Row totals Allergic history 60 30 30 120 not allergic 220 10 50 280 columns totals 280 40 80 400

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