1. A noted psychic was tested for ESP. The psychic was presented with 400 cards face down and asked to determine if each card was matched with one of four symbols: a star, cross, circle, or square. The psychic was correct in 120 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. How large a sample n would you need to estimate p with margin of error 0.01 with 95% confidence? Use the guess p = 0.25 as the value for p.
A. n = 1351
B. n = 7203
C. n = 9604
2. A sociologist is studying the effect on the divorce rate of having children within the first three years of marriage. From city marriage records she selects a random sample of 400 couples who were married between 1985 and 1990 for the first time, with both members of the couple between 20 and 25. Of the 400 couples, 220 had at least one child within the first three years of marriage. Of the couples who had children, 83 were divorced within 5 years, while in the couples who didn't have children within three years only 52 were divorced. Suppose p1 is the proportion of couples married in this time-frame who had a child within the first three years and were divorced within five years, and p2 is the proportion of couples married in this time-frame who did not have a child within the first three years and were divorced within five years. The estimate of µD = p1 - p2 is
A. 0.0884.
B. 0.3100.
C. 0.3375.
3. An SRS of 100 of a certain popular model car in 1993 found that 20 had a certain minor defect in the brakes. An SRS of 400 of this model car in 1994 found that 50 had the minor defect in the brakes. Let p1 and p2 be the proportion of all cars of this model in 1993 and 1994, respectively, that actually contain the defect. A 90% confidence interval for p1 - p2 is
A. 0.075 ± 0.084.
B. 0.075 ± 0.071.
C. 0.075 ± 0.043.