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.
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Cotton:
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48.82
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48.88
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48.98
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49.04
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48.68
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49.34
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48.75
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49.12
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Ramie:
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41.72
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41.83
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42.05
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41.44
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41.27
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42.27
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41.12
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41.49
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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: