4.3. In 2000, the GSS asked subjects whether they are a member of an environmental group (variable GRNGROUP) and whether they would be very willing to pay much higher prices to protect the environment (variable GRNPRICE). Table 4.4 shows results.

(a) Explain why 96/1117 = 0.086 estimates the probability that a randomly selected American adult is a member of an environmental group.

(b) Show that the estimated probability of being very willing to pay much higher prices to protect the environment is (i) 0.312, given that the person is a member of an environmental group, (ii) 0.086, given not a member of an environmental group.

(c) Show that the estimated probability a person is both a member of an environmental group and very willing to pay much higher prices to protect the environment is 0.027 (i) directly using the counts in the table, (ii) using the probability estimates from

(a) and (b).

(d) Show that the estimated probability that a person answers yes to both questions or no to both questions is 0.862.

TABLE 4.4 Pay Higher Prices Yes No Total Member of Yes 30 66 96 Environmental No 88 933 1021 Group Total 118 999 1117