Manager examined potential differences between two models of bicycles. The mean life of the bicycles is of primary concern. The followings table provides the available date which measured in thousands of miles:
Sample size Sample mean Sample standard deviation
Model A $80$ $50.2$ $2.6$
Model B $64$ $47.8$ $4.0$
I know how to test a mean, but how to determine by using an appropriate hypothesis whether the mean lives of the two brands are different? To create a new random variable $A-B$ and see whether $A-B=0$? (denote the mean life of Model A by $A$, and that of Model B by $B$) Also which two appropriate significance levels should I test at?
Should I assume they are normally distributed?
How about to determine whether the mean life of the bicycles of model B is longer than that of the model A bicycles? Is it correct to test whether $B-A>0$? (denote the mean life of Model A by $A$, and that of Model B by $B$)