slide10 - Diff of Means Var known Null hypothesis Test...

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1 Diff of Means, Var known Null hypothesis: Test statistic: 0 1 2 0 : H µ µ = ∆ 1 2 0 0 2 2 1 2 1 2 X X Z n n σ σ − ∆ = + 2 Example Hermione hypothesizes that the tulips in her garden are, on average, 2 inches taller than the crocuses. By taking some measurements, she knows that her 28 tulips have an average height of 8 inches (and standard deviation 1.5), while the 33 crocuses have an average height of 5 inches (and standard deviation 1).
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3 Questions I Test the hypothesis at the 5% level. What is the P-value? Give the 95% confidence interval for the difference in the two means. 4 Confidence Intervals The 100(1– α )% confidence interval on the difference of two means is: 2 2 2 2 1 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 x x z x x z n n n n α α σ σ σ σ µ µ + + +
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5 Required Sample Size (a) For the two-sided alternate hypothesis with significance level α , the sample size n 1 = n 2 = n required to detect a true difference in means of with power at least 1– β is: 2 0 2 2 2 1 2 / ) ( ) )( z z ( n σ σ β α + + = 6 Required Sample Size (b) If variances are known, and sample sizes are equal, the required sample size to guarantee an error no more than E at 100(1– α ) percent confidence is: ( ) 2 2 2 1 2 z n E α σ σ = +
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7 Questions II
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