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Fabrics respond differently to the same dye. Clothing manufacturers need to be able to match the colors of different fabrics. A researcher dyed samples of cotton and of ramie with a dye called procion blue, applied in the same way to each sample. Then she measured the lightness of the color with a colorimeter on a scale in which black is 0, white is 100. Here are the data for 8 pieces of each fabric.
Cotton:
48.82
48.88
48.98
49.04
48.68
49.34
48.75
49.12
Ramie:
41.72
41.83
42.05
41.44
41.27
42.27
41.12
41.49
Evidently one procedure gives darker colors than the other. Make a confidence interval estimate for the mean darkness of cotton minus the mean darkness of ramie after this dye procedure. Use 99% as your confidence level.
Lower Confidence Level:
Upper Confidence Level:
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