A health official takes a two-phase sample to estimate the prevalence of diabetes in a population. In phase I, an SRS of size 1000 is taken from the population of size 100,000, and each individual is asked demographic information and whether he or she has diabetes. It is known that some demographic groups are more at risk for diabetes than others; in addition, the self report of diabetes may be inaccurate. Therefore, each individual in the phase II sample is given a medical exam to determine diabetes status. The phase I sample is divided into 4 strata. Stratum h has nh observations in the phase I sample and mh observations in the phase II sample. After the medical exam, rh persons in stratum h of the phase II sample were determined to have diabetes.

Estimate the total number of persons with diabetes in the population, along with its standard error.

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Stratum High risk group and reports diabetes High risk group and does not report diabetes 3 45 17 Low risk group and reports diabetes Low risk group and does not report diabetes 472 47 8 Ih nh 241 96 86 174 35 29