A crayon manufacturer is comparing the effects of two kinds of yellow dye on the
ID: 3132321 • 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 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 exceeds that of crayons made with dye A by more than 1 J? A. No, we cannot conclude that the mean strength of crayons made with dye B exceeds that of crayons made with dye A by more than 1 J. B. Yes, we can conclude that the mean strength of crayons made with dye B exceeds that of crayons made with dye A by more than 1 J.Explanation / Answer
Let ud = u2 - u1.
Formulating the null and alternative hypotheses,
Ho: ud <= 1
Ha: ud > 1
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 = 0.724673385
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 0.362336693
Calculating the mean of the differences (third column):
XD = 0.65
As t = [XD - uD]/sD, where uD = the hypothesized difference = 1 , then
t = -0.965952406
As df = n - 1 = 3
hence, using p values,
p = 0.20266089
As P is large, WE FAIL TO REJECT THE NULL HYPOTHESIS.
Hence,
OPTION A: No, we cannot conclude that the mean strength of crayons made with dye B exceeds that of crayons made with dye A by more than 1 J.
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