Two different analytical tests can be used to determine the impurity level in steel alloys. Eight specimens are tested using both procedures, and the results are shown in the following tabulation.

(a) Is there sufficient evidence to conclude that tests differ in the mean impurity level, using α = 0.01?

(b) Is there evidence to support the claim that test 1 generates a mean difference 0.1 units lower than test 2? Use α = 0.05.

(c) If the mean from test 1 is 0.1 less than the mean from test 2, it is important to detect this with probability at least 0.90. Was the use of eight alloys an adequate sample size? If not, how many alloys should have been used?

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Specimen Test 1 Test 2 1.2 1.4 2 1.3 1.7 3 1.5 1.5 1.4 1.3 5 1.7 2.0 1.8 2.1 1.4 1.7 8 1.3 1.6