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37016 2940 3407639956 slide 14

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Unformatted text preview: The Confidence Interval for µ ( σ is known) s Solution • The parameter to be estimated is µ , the mean demand µ, the mean demand during lead time. • We need to compute the interval estimation for µ. • From the data provided in previous slide, the sample mean is x = 370.16. x ± zα 2 σ n = 37016± z.025 . 75 25 75 25 Since 1 - α =.95, α = .05. Thus α /2 = .025. Z.025 = 1.96 = 37016±1.96 . = 37016± 2940= [ 3407639956 . . ., .] Slide 14 The Confidence Interval for µ ( σ is unknown) s Replace σ by s P ( x − zα 2 s s ≤ µ ≤ x + zα 2 ) = 1 −α n n The confidence interval s (Note: Textbook uses t instead of z. t means using t distribution. By CLT, you can still use z; however t is “better”! We’ll discuss t in a few slides later.) Slide 15 The Width (Margin of Error) of Confidence Interval The width (margin of error) of the confidence interval is affected by • the population standard deviation (σ) • the confidence level (1-α) • the sample size (n). Slide 16 Determining the Sample Size s We can control the margin of error of the confidence interval by changing the sample size. Thus, w...
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