2. Two different analytical tests can be used to determine the impurity levels in steel alloys. The first test is known to perform very well but the second is cheaper. A specialty steel manufacturer will adopt the second method unless there is evidence that it gives significantly different results than the first. Eight steel specimens are cut in half and one half is randomly assigned to one test and the other half to the other test. The results are shown in the following table.

(a) State the appropriate null and alternative hypotheses.

(b) Carry out the paired data T test at level α = 0.05, and state whether H0 is rejected or not. Should the specialty steel manufacturer adopt the second method?

(c) Construct a 95% CI for the mean difference.

Specimen Test 1 Test 2 1 1.2 1.4 23 2 1.3 1.7 1.5 1.5 4 1.4 1.3 5 1.7 2.0 19 6 1.8 2.1 7 1.4 1.7 8 1.3 1.6