Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. The following is the amount $($$$000)$ earned per month by a sample of $15$ Claiborne models:

$$5\mathrm{.}6$ $$6\mathrm{.}3$ $$6\mathrm{.}2$ $$3\mathrm{.}2$ $$7\mathrm{.}0$ $$6\mathrm{.}8$ $$4\mathrm{.}0$ $$3\mathrm{.}7$ $$3\mathrm{.}4$ $$6\mathrm{.}1$

$$4\mathrm{.}1$ $$4\mathrm{.}8$ $$6\mathrm{.}5$ $$3\mathrm{.}1$ $$4\mathrm{.}0$

The following is the amount $($$$000)$ earned by a sample of $12$ Klein models.

$$2\mathrm{.}9$ $$3\mathrm{.}9$ $$4\mathrm{.}8$ $$6\mathrm{.}2$ $$1\mathrm{.}8$ $$2\mathrm{.}6$ $$3\mathrm{.}5$ $$3\mathrm{.}6$ $$3\mathrm{.}7$ $$3\mathrm{.}1$

$$2\mathrm{.}1$ $$2\mathrm{.}0$ Is it reasonable to conclude that Claiborne models earn more? Use the $0\mathrm{.}01$ significance level and assume the population standard deviations are not the same. Find the degrees of freedom for unequal variance test. $($Round down your answer to the nearest whole number.$).$ c$.$ Compute the value of the test statistic. $($Round your answer to $3$ decimal places.$).$ d$.$ Is it reasonable to conclude that Claiborne models earn more? Use the $0\mathrm{.}01$ significance level.