In an experiment used to test the hardness reading associated with two tips of a

Question

In an experiment used to test the hardness reading associated with two tips of a machine that presses a rod with a pointed tip in a manufacturing process, pair samples of hardness readings for the two tips are paired according to the metal rod that is pressed (each rod is pressed with each tip once). Ten metal rods are pressed and the table below summarizes the results:

7 3 3 3 8 3 2 9 5 4

5 2 4 2 9 2 2 7 3 4

Test the hypothesis for the mean difference in hardnesses given by H0:d = 0 at the 10% significance level where d is the true mean d difference in hardness reading over all possible specimens.

Explanation / Answer

Ans:

Test statistic:

t=(0.7-0)/(1.160/sqrt(10))=1.909

df=10-1=9

p-value(2 tailed)=tdist(1.909,9,2)=0.0886

As,p-value=0.0886<0.1,we reject null hypothesis.

There is sufficient evidence to conclude that mean difference is not equal to zero.

tip 1 tip 2 difference 1 7 5 2 2 3 2 1 3 3 4 -1 4 3 2 1 5 8 9 -1 6 3 2 1 7 2 2 0 8 9 7 2 9 5 3 2 10 4 4 0 mean= 0.7 std. dev.= 1.160

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