Hypothesis testing for the difference between two means (variances are known)?
Question: A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by more than 12 kg. To test this claim, 50 pieces of each type of thread were tested under similar conditions. Type A thread had an average tensile strength of 86.7 kg with a standard deviation of 6.28 kg, while type B thread had an average tensile strength of 77.8 kg with a standard deviation of 5.61 kg. Test the manufacturer's claim using a 0.05 level of significance.
Problem: Which of these should be the correct hypothesis tests?
H0 : uA - uB = 12
H1: uA - uB < 12
OR
H0: uA - uB = 12
H1: uA - uB > 12
The reason for my confusion is that the null hypothesis must always be represented by an equality, and the alternate hypothesis is always the exact opposite of the null. This would then mean that the second set of hypotheses are true. But the test statistic turns out to be negative, hence I am led to believe that the test should be a left tail instead, as indicated by the first set of hypotheses.
Which set of hypotheses is the more logical one to use, and why?