The following are the Brinell hardness values obtained for thesamples of two mag

Question

The following are the Brinell hardness values obtained for thesamples of two magnesium
alloys
Alloy1       Alloy 2
66.3           71.3
63.5           60.4
64.9           62.6
61.8           63.9
64.3           68.8
64.7           70.1
65.1           64.8
64.5           68.9
68.4    65.8
63.2            66.2

Assuming the measurement system has a normal distribution, test thetwo-sided test of
hypothesis for

Suppose it is known that the differences rather than the individualmeasurement are of
importance (that is D=Alloy 2-Alloy 1, that is: D = 2-1), then let:
H0: D=3,
H1: D < 3
Test the hypothesis. Will you reject or not reject the nullhypothesis at ?=0.05

Explanation / Answer

The differences are given below: 5 -3.1 -2.3 2.1 4.5 5.4 -.3 4.4 -2.6 3 For this test, with .05 as the tail probability and 10-1=9degrees of freedom, we get -1.833 as thet* The sample mean of differences is 1.61, and standarddeviation is 3.383112. The standard deviation of the sample meanswill be Sx/n = (3.383112/10)=1.0698 Use z-score of the differences: (1.61-3)/1.0698=-1.2993standard devations from the mean. That is the t-value. p-value is .11307 with software, so at =.05, we do notreject the null hypothesis. p-value is .11307 with software, so at =.05, we do notreject the null hypothesis.

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