A sociological study carried out in a village is interested in the proportion of households whose least one member is over the age of 65. The village has 621 households according to the directory most recent municipal. A simple random sample of n = 60 households was selected in the directory. At the end of the fieldwork, out of the 60 households sampled, there were only 11 that contained at least one member over the age of 65.

(a) Give an estimate of the true proportion p of households with at least one member is over 65 years old in the village. (b) What is the margin of error on the estimate in a)? (c) Construct a confidence interval of p at about 95%. (d) What sample size should be used in order to estimate p with a margin of error on the estimate of 0.08? Assume that the real proportion p 0.2