Claim: \(\mu_{1} \geq \mu_{2} ; \alpha=0.01\). Assume \(\sigma_{1}^{2}=\sigma_{2}^{2}\)

Sample statistics: \(\bar{x}_{1}=44.5, s_{1}=5.85, n_{1}=17\) and

\[ \bar{x}_{2}=49.1, s_{2}=5.25, n_{2}=18 \]

Test the claim about the difference between two population means \(\mu_{1}\) and \(\mu_{2}\) at the level of significance \(\alpha\). Assume the samples are random and independent, and the populations are normally distributed.