Test the given claim using the $\alpha = 0.01$ significance level and assuming that the populations are normally distributed.
Claim: The treatment population and the placebo population have the same mean.
Treatment group: $n = 9,$ $\overline{x} = 123,$ $s=5.5.$
Placebo group: $n = 7,$ $\overline{x}=113,$ $s=5.3.$

(a) The test statistic is .

(b) What is the conservative estimate for the degrees of freedom? df =

(c) The negative critical value is .

(d) The positive critical value is .

(e) Is there sufficient evidence to warrant the rejection of the claim that the treatment and placebo populations have the same mean?

A. Yes
B. No