Final answer:
With a 95 percent confidence level, the estimated percentage of households with at least one unemployed adult is between 5.64 percent and 18.36 percent. To estimate the percentage of households in the area in which at least one adult is unemployed, we can use the formula for a confidence interval for a proportion.
Step-by-step explanation:
To estimate the percentage of households in the area in which at least one adult is unemployed, we can use the formula for a confidence interval for a proportion. Given that there are 12 households out of 100 with at least one unemployed adult, we can calculate the sample proportion as 12/100 = 0.12. Using the formula for a confidence interval for a proportion, we can calculate the standard error as sqrt((0.12 * (1-0.12)) / 100) = 0.0324. With a 95 percent confidence level, we need to find the z-score corresponding to a 2.5 percent tail area, which is approximately 1.96. Now we can calculate the margin of error as 1.96 * 0.0324 = 0.0636. Finally, the confidence interval can be calculated as 0.12 ± 0.0636, resulting in a range of approximately 0.0564 to 0.1836. Therefore, we can estimate that the percentage of households in the area with at least one unemployed adult is between 5.64 percent and 18.36 percent.