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. Claim: \( \mu_{1}=\mu_{2} ; \alpha=0.10 \). Assume \( \sigma_{1}^{2}=\sigma_{2}^{2} \) Sample statistics: \( \bar{x}_{1}=35.2, s_{1}=3.5, n_{1}=14 \) and \[ \bar{x}_{2}=37.4, s_{2}=2.2, n_{2}=18 \] \( \begin{array}{ll}\text { Identify the null and alternative hypotheses. Choose the correct answer below. } \\ H_{0}: \mu_{1}=\mu_{2} & \text { B. } H_{0}: \mu_{1}>\mu_{2} \\ H_{a}: \mu_{1} \neq \mu_{2} & H_{a}: \mu_{1} \leq \mu_{2} \\ \text { C. } H_{0}: \mu_{1} \leq \mu_{2} & \text { D. } H_{0}: \mu_{1} \geq \mu_{2} \\ H_{a}: \mu_{1}>\mu_{2} & H_{a}: \mu_{1}<\mu_{2} \\ \text { E. } H_{0}: \mu_{1} \neq \mu_{2} & H_{0}: \mu_{1}<\mu_{2} \\ H_{a}: \mu_{1}=\mu_{2} & H_{a}: \mu_{1} \geq \mu_{2}\end{array} \)
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