Curry Sherman
09/11/2024 · Junior High School
Test the claim about the difference between two population means \( \mu_{1} \) and \( \mu_{2} \) at the level of significance \( \alpha \). Assume t samples are random and independent, and the populations are normally distributed. Claim: \( \mu_{1}=\mu_{2} ; \alpha=0.01 \). Assume \( \sigma_{1}^{2}=\sigma_{2}^{2} \) Sample statistics: \( \bar{x}_{1}=31.1, s_{1}=3.6, n_{1}=10 \) and \( \bar{x}_{2}=32.2, s_{2}=2.2, n_{2}=19 \)
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The test statistic \( t \approx -1.025 \) falls within the critical range, so we fail to reject the null hypothesis. At the \( \alpha = 0.01 \) significance level, there is not enough evidence to conclude that the means of the two populations are different.
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