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

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1 Diff of Means, Var known ± Null hypothesis: ± Test statistic: 01 2 0 : H µµ −= 12 0 0 22 XX Z nn σσ −− = + 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: 22 12 2 1 212 2 xxz nn αα σσ µµ −− + ≤− ≤−+ +
5 Required Sample Size (a) ± For the two-sided alternate hypothesis with significance level α , the sample size n 1 = 2 = 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 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 22 12 z n E σσ  =+  

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7 Questions II ±
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## This note was uploaded on 05/05/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

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

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