Chapter3 - 1 Comparing Systems 13/10/2009 1 R. Jain book +...

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Unformatted text preview: 1 Comparing Systems 13/10/2009 1 R. Jain book + M. Claypool [WPI] Sample versus Population-1 • The word “sample” comes from the same root word as “example” word as example • Similarly, one sample does not prove a theory, but rather is an example • Basically, a definite statement cannot be made about characteristics of all systems 2 • Instead, make probabilistic statement about range of most systems – Confidence intervals 2 Sample versus Population-2 • Say we generate 1-billion random numbers ! mean µ and stddev σ – mean µ and stddev σ . – µ is population mean – That is, µ and σ are the “ True ” values • Put the numbers in a pool, draw sample of size n – Sample {x 1 , x 2 , …, x n } has mean , and stddev s – That is, and s are the “ measured ” values 3 • It is likely to have ≠ µ and s ≠ σ • Typically, µ is not known and may be impossible to know – Instead, get estimate of µ from Confidence Interval for the Mean • Obtain probability of µ in interval [c 1 ,c 2 ] Prob{c < µ < c } = 1 α – Prob{c 1 < µ < c 2 } = 1- α • (c 1 , c 2 ) is called confidence interval • α is called significance level • (1- α ).100% is called confidence level • Typically we want α small so that confidence level is high – Say, α =0.1 ⇒ 90% confidence level 4 ∴ the interval (c 1 , c 2 ) contains the value µ with 90% confidence level or with probability = 0.9 µ c 1 c 2 3 Determining Confidence Interval • 100(1- α ) % confidence interval for n observations is observations is: • t [ α /2; n-1] = α /2-entry in the t-table with n-1 degrees of freedom (Student’s t distribution Table “Student” was an anonymous name 5 Table. Student was an anonymous name) 6 4 Example 1 • = 3.90, s = 0.95 and n = 30 • A 90% confidence interval for the mean ( α =0.1) = 3.90 ± 1.699 × 0.95 / = (3.61, 4.19) 30 3.9 3.9 4 1 1.9 2.7 2 8 (Sorted) CPU Time • We can state with 90% confidence that the population mean is between 3.61 and 4.19 The chance of error in this statement is 10%....
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This note was uploaded on 10/27/2010 for the course CMPE 474 taught by Professor Muhammedsalamah during the Spring '10 term at Eastern Mediterranean University.

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Chapter3 - 1 Comparing Systems 13/10/2009 1 R. Jain book +...

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