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Unformatted text preview: A List of Hypothesis Tests 1. Tests for the population mean, μ i) Large Sample Size, 30 n ≥ a) Test H : μ μ = against H 1 : μ μ ≠ At the α significance level, reject H if 2 1 x z n α μ σ If σ 2 is unknown, replace by the sample variance s 2 b) Test H : μ μ = against H 1 : μ μ At the α significance level, reject H if 1 x z n α μ σ If σ 2 is unknown, replace by the sample variance s 2 c) Test H : μ μ = against H 1 : μ μ < At the α significance level, reject H if 1 x z n α μ σ <  If σ 2 is unknown, replace by the sample variance s 2 ii) Small Sample Size, 30 n < Here we must assume that the original population is Normal . If σ 2 is known, we can carry out one or twosided tests as for the large sample case above. However, if σ 2 is unknown, we cannot replace by the sample variance s 2 , as in the large sample case, but must use ttests. a) Test H : μ μ = against H 1 : μ μ ≠ At the α significance level, reject H if 2 1 x t s n α μ where 2 t α has n1 degrees of freedom 1 b) Test H : μ μ = against H 1 : μ μ At the α significance level, reject H if 1 x t s n α μ where t α has n1 degrees of freedom c) Test H : μ μ = against H 1 : μ μ < At the α significance level, reject H if 1 x t s n α μ <  where t α has n1 degrees of freedom COMPUTATION NOTE: If the sample size is large, but σ 2 is unknown, the Normal test in section i) is equivalent to the ttest in section ii) and the conclusions are the same. If you are using Minitab for calculation, and σ 2 is unknown, use the ttest for both large and small samples....
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This note was uploaded on 04/07/2012 for the course IBE 340 taught by Professor Valerieozaki during the Spring '09 term at Sophia University.
 Spring '09
 ValerieOzaki

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