A crayon manufacturer is comparing the effects of two kinds of yellow dye on the
ID: 3132320 • Letter: A
Question
A crayon manufacturer is comparing the effects of two kinds of yellow dye on the brittleness of crayons. Dye B is more expensive than dye A, but it is thought that it might produce a stronger crayon. Four crayons are tested with each kind of dye, and the impact strength (in joules) is measured for each. The results are as follows: Can you conclude that the mean strength of crayons made with dye B is greater than that of crayons made with dye A ? A. No, we cannot conclude that the mean strength of crayons made with dye B is greater than that of crayons made with dye A. B. Yes, we can conclude that the mean strength of crayons made with dye B is greater than that of crayons made with dye A.Explanation / Answer
Let ud = u2 - u1.
Formulating the null and alternative hypotheses,
Ho: ud <= 0
Ha: ud > 0
At level of significance = 0.01
As we can see, this is a right tailed test.
Calculating the standard deviation of the differences (third column):
s = 0.680184912
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 0.340092456
Calculating the mean of the differences (third column):
XD = 1.025
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = 3.013886316
As df = n - 1 = 3
Hence, using p values,
p = 0.028517649
As P < 0.05, WE REJECT THE NULL HYPOTHESIS.
hence,
OPTION B: YES, we can conclude that the mean strength of crayons made with dye B is greater than that of crayons made with dye A. [ANSWER]
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