Fabrics respond differently to the same dye. Clothing manufacturers need to be a

Question

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 96% as your confidence level.

Lower Confidence Level:

Upper Confidence Level:

Explanation / Answer

Total Mean Std dev X Cotton 48.82 48.88 48.98 49.04 48.68 49.34 48.75 49.12 391.61 48.95125 0.215369 Y Ramie 41.72 41.83 42.05 41.44 41.27 42.27 41.12 41.49 333.19 41.64875 0.392189 Group   Group One     Group Two   Mean 48.951 41.649 SD 0.215 0.398 SEM 0.07601 0.14071 N 8        8        df = 7   standard error of difference = 0.160 For 96% z value = 2.05 Margin of error 0.328 Mean difference 7.3025 Confidence interval lower bound 6.9745 Confidence interval upper bound 7.6305

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