Two different analytical tests can be used to determine the impurity level in steel alloys. Six specimens are used and both tests are applied to determine the impurity level for each specimen in the sample. The observed data is as below.
Specimen: 1 2 3 4 5 6
Test 1: 1.2. 1.3. 1.5. 1.4. 1.7. 1.8
Test 2: 1.4. 1.7. 1.5. 1.3. 2.0. 2.2
a) Is there sufficient evidence to conclude that the two tests give different true mean impurity levels? Carry out an appropriate test of hypothesis by using the p-value and draw your conclusions.
b) Name the type of error you might have committed in the decision you made above.