Hypothesis testing for difference between variances, population means and paired.
Five samples of a ferrous-type substance are to be used to determine if there is a difference between a laboratory chemical analyses and X-ray fluorescent analysis of the iron content. Each sample was split into two subsamples and the two types were applied. Following are the coded data showing the iron content analysis.
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Sample
|
|
Analysis
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1
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2
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3
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4
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5
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X-ray (B)
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2.0
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2.0
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2.3
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2.1
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2.4
|
|
Chemical (A)
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2.2
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1.9
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2.5
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2.3
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2.4
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Assuming the measurement system has a normal distribution, test thetwo-sided test of hypothesis for
a) H0: σA2 = σB2 at α =0.05,
b) H0: μB -μA= 28% at α =0.1
c) Suppose it is desired to test the hypothesis that the differences rather than the individual measurement are of importance, (that is D=B-A, that is: μD = μB -μA), then let:
H0: μD=10%,
H1: μD < 10%
Test the hypothesis. Will you reject or not reject the null hypothesis at α = 0.05