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 portion 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. Do these samples provide evidence significant at the 5% level that the dye affects the cotton and ramie fabrics differently? Formulate H_0 and H_a. a. Give the test statistic: | b. Give the P-value: c. Your decision for the hypothesis test: A. Do Not Reject H_0. B. Reject H_a. C. Reject H_0. D. Do Not Reject H_a.

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Cotton and Ramie
H0 : D = 0
HA : D 0
Hypothesis test results:

Hence,

a) 69.845214

b) 0

c) Option C; Reject Ho.

Difference Mean Std. Err. DF T-Stat P-value Cotton - Ramie 7.3025 0.10455262 7 69.845214 <0.0001

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