Determining alcoholic fermentation in wine is critical to the wine-making process. Must/wine density is a good indicator of the fermentation point because the density value decreases as sugars are converted into alcohol. For decades, winemakers have measured must/wine density with a hydrometer. Although accurate, the hydrometer employs a manual process that is very time-consuming. Consequently, large wineries are searching for more rapid measures of density measurement. An alternative method uses the hydrostatic balance instrument (similar to the hydrometer but digital). A winery in Portugal collected the must/wine density measurements for white wine samples randomly selected from the fermentation process for a recent harvest. For each sample, the density of the wine at 20°C was measured with both the hydrometer and the hydrostat balance. The densities for 40 wine samples are saved in the file. The first five and last five observations are shown in the table. The winery will use the alternative method of measuring wine density only if it can be demonstrated that the mean difference between the density measurements of the two methods does not exceed .002. Perform the analysis for the winery. Provide the winery with a written report of your conclusions.

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Sample Hydrometer Hydrostatic 1.08655 1.00270 101393 1.09467 1.10263 1.09103 1.00272 1.01274 1.09634 110518 108084 109452 0.99479 1.00968 1.00684 1.08097 1.09431 0.99498 1.01063 100526 36 38 39 40