Question

an introduction to biostatistics third edition

VU 1 IDD While DDT (dichlorodiphenyltrichloroethane) has been banned for use as an insec- ide in the United States since 1972 because of damage to non-target species, it will used in some countries and persists in the environment. The following table Characterizes 1000 cores taken from an arctic ice sheet. Each sample was tested for levels of DDT and its breakdown products DDE (dichlorodiphenyldichloroethy- lene) and DDD (dichlorodiphenyldichloroethane). In addition each core was also tested for nitrates. For each type of contaminant the core was scored as high, moderate, or low. DDT, DDE, DDD High Moderate Low Total Nitrates High Moderate Low 105 70 25 80 175 45 55 145 300 240 390 370 Total 200 300 500 1000 Calculate the following probabilities for an ice core picked at random from this group. (a) It has high levels of nitrate. (6) It has high levels of both nitrates and DDT. (C) It has high levels of nitrates given low levels of DDT. (d) It has moderate levels of nitrates given low levels of DDT. (e) Find the probability that two cores picked at random will both have moderate levels of DDT. Think about sampling without replacement here. ) Are high levels of nitrates and low levels of DDT independent of each other?

Answer 1

a)P(high level of nitrate)=240/1000 =0.24

b) P(high level of nitrate and DDT)=105/1000=0.105

c)P(high level of Nitrate|low level of DDT) =55/500=0.11

d) P(Moderate level of Nitrate|low level of DDT) =145/500=0.29

e) P(both have moderate level of DDT) =(500/1000)*(499/999)=0.24975

f) as P(high level of nitrate) is not equal to P(high level of Nitrate|low level of DDT) , therefore events high level of nitrate and low levels of DDT are not independent,