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Supposing that the following sample of 10 numbers arise from the Normal distribution with mean μ and standard deviation σ = 6.3, obtain, from first principles, 95% and 99% confidence intervals for μ.  39.1 21.2 38.3 24.9 25.6 26.2 31.5 34.6 24.5 22.4  

Measure a test statistic for null hypothesis H0 : μ = 30 against the two-sided alternative hypothesis H1 : μ ≠ 30, and by plotting this on its reference distribution, recognize and compute the corresponding p-value associated with H0. What are your conclusions about H0?

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