In a certain province, a researcher plans to conduct a household survey to estimate the average number of out-of-school youths (7-20 years old who are not enrolled in school the last two school years) among poor households. There is no list of poor and non-poor households in the province and their respective numbers are unknown. The researcher plans to draw first a sample of barangays from a list in the province via SRSWOR and then, in each sample barangay, a sample of households will be drawn via systematic sampling. Assume the total number of households in a barangay is known. The sample households will in turn be interviewed for information that will classify them as poor or non-poor, as well as information on their number of out-of-school youths.

Formulate the estimator for the mean number of out-of-school youths among poor households in the province.

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