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Statistical Analysis on Dyes

The color of a fabric depends on the dye used and also how the dye is applied. This matters to clothing manufacturers, who want the color of the fabric to be just right. The study discussed in the previous exercise went on to dye fabric made of ramie with the same "procion blue" dye applied in two different ways. Here are the lightness scores for 8 pieces of identical fabric dyed in each way:
Method B 40.98 40.88 41.30 41.28 41.66 41.50 41.39 41.27
Method C 42.30 42.20 42.65 42.43 42.50 42.28 43.13 42.45

a) This is a randomized comparative experiment. Outline the design.

b) A clothing manufacturer wants to know which method gives the darker color(lower lightness score). Use sample means to answer this question. Is the difference between the two sample means statistically significant? Can you tell from just the P-value whether the difference is large enough to be important in practice?

Solution Preview

Please see the attached file.

Hypotheses: H0: m1 = m2 vs. HA: m1 ¹ m2
Level of Significance: a = 5%
Decision Rule: Reject the null hypothesis if p-value < 0.05
Method B Method ...

Solution Summary

This solution conducts a statistical analysis on the lightness scores of the dyed fabric by outlining the design, providing a null and alternative hypothesis, calculating the test statistic and comparing to to the p-value. A decisions is made to determine if the difference between the two sample means is significant.