Math  /  Data & Statistics

QuestionUse the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether μ1>μ2\mu_{1}>\mu_{2} at the α=0.05\alpha=0.05 level of significance for the given sample data. (b) Construct a 99%99 \% confidence interval about μ1μ2\mu_{1}-\mu_{2}. \begin{tabular}{ccc} & Population 1 & Population 2 \\ \hline n\mathbf{n} & 22 & 15 \\ \hlinex\overline{\mathbf{x}} & 50.7 & 42.1 \\ \hline s\mathbf{s} & 4.6 & 10.6 \end{tabular} (a) Identify the null and alternative hypotheses for this test. A. H0:μ1=μ2H_{0}: \mu_{1}=\mu_{2} B. H0:μ1>μ2H_{0}: \mu_{1}>\mu_{2} C. H0:μ1μ2H_{0}: \mu_{1} \neq \mu_{2} H1:μ1<μ2H_{1}: \mu_{1}<\mu_{2} H1:μ1=μ2H_{1}: \mu_{1}=\mu_{2} H1:μ1=μ2H_{1}: \mu_{1}=\mu_{2} D. H0:μ1<μ2H_{0}: \mu_{1}<\mu_{2} E. H0:μ1=μ2H_{0}: \mu_{1}=\mu_{2} F. H0:μ1=μ2H_{0}: \mu_{1}=\mu_{2} H1:μ1=μ2H_{1}: \mu_{1}=\mu_{2} H1:μ1μ2H_{1}: \mu_{1} \neq \mu_{2} H1:μ1>μ2H_{1}: \mu_{1}>\mu_{2}

Studdy Solution
(a) We reject the null hypothesis and conclude that μ1>μ2\mu_1 > \mu_2 at the 0.05 significance level. (b) The 99% confidence interval for μ1μ2\mu_1 - \mu_2 is approximately (0.044,17.244)(-0.044, 17.244).

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