Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples.
Sample 1: $n_1=12, \ \overline{x}_1=12, \ s_1=5$.
Sample 2: $n_2=21, \ \overline{x}_2=5, \ s_2=3$.

(a) The test statistic is

(b) Find the t critical value for a significance level of $0.05$ for an alternative hypothesis that the first population has a larger mean (one-sided test): $t^* =$

(c) The conclusion is

A. There is not sufficient evidence to warrant rejection of the claim that the two populations have the same mean.
B. There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and accept that the first population has a larger mean.