Wells Schneider
02/22/2023 · Middle School
Test the claim about the difference between two population means \( \mu_{1} \) and \( \mu_{2} \) at the level of significance \( \alpha \). Assume th 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 \[ \bar{x}_{2}=37.4, s_{2}=2.2, n_{2}=18 \]
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To test the claim that \( \mu_{1} = \mu_{2} \) with \( \alpha = 0.10 \), use the two-sample t-test. Given the sample statistics, calculate the t-statistic and compare it to the critical t-value for \( \alpha = 0.10 \) and 30 degrees of freedom. If the t-statistic is less than the critical value, reject the null hypothesis.
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