Suppose the confidence interval obtained in Problem 9.24 is considered to be too wide for practical purposes (i.e., it is lacking in precision). Instead, we desire that the 95 percent confidence...

Suppose the confidence interval obtained in Problem 9.24 is considered to be too wide for practical purposes (i.e., it is lacking in precision). Instead, we desire that the 95 percent confidence interval be within two percentage points of the true percentage of households with at least one adult unemployed. What is the minimum sample size required to satisfy this specification (a) if we make no assumption about the true percentage before collecting a larger sample and (b) if, on the basis of the sample collected in Problem 9.23, we assume that the true percentage is no larger than 18 percent?

Problem 9.24

For a random sample of 100 households in a large metropolitan area, the number of households in which at least one adult is currently unemployed and seeking a full-time job is 12. Estimate the percentage of households in the area in which at least one adult is unemployed, using a 95 percent confidence interval.