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Data Collectionhard
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A survey estimates average electricity consumption (yˉsample=850\bar{y}_{sample} = 850yˉ​sample​=850 kWh). The known population mean for a correlated auxiliary variable (degree-days) is Xˉpop=2000\bar{X}_{pop} = 2000Xˉpop​=2000, while xˉsample=1950\bar{x}_{sample} = 1950xˉsample​=1950. Using a calibration estimator: yˉcal=yˉsample+β(Xˉpop−xˉsample)\bar{y}_{cal} = \bar{y}_{sample} + \beta(\bar{X}_{pop} - \bar{x}_{sample})yˉ​cal​=yˉ​sample​+β(Xˉpop​−xˉsample​)

with regression coefficient β=0.40\beta = 0.40β=0.40 (electricity vs. degree-days), what is the calibrated estimate?