A product developer is interested in reducing the drying time of a primer paint. Two formulations of the paint are tested; formulation $1$ is the standard chemistry, and formulation $2$ has a new drying ingredient that should reduce the drying time. From experience, it is known that the standard deviation of drying time is $8$ minutes, and this inherent variability should be unaffected by the addition of the new ingredient. Ten specimens are painted with formulation $1,$ and another $10$ specimens are painted with formulation $2$; the $20$ specimens are painted in random order. The two sample average drying times are $121$ minutes and $112$ minutes, respectively. What is the alternative hypothesis should be used here to determine the effectiveness of the new ingredient, using alpha $0\mathrm{.}05?$

A$.$ population $1>=$ population $2$

B$.$ population $1=$ population $2$

C$.$ population $1<$ population $2$

D$.$ population $1>$ population $2$