MATH 226 - 11.5.07

# MATH 226 - 11.5.07 - .1 ) = 1 = .9 o So z .1 = 1.28 using...

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MATH 226 – November 5, 2007 Confidence Intervals o A 90% confidence interval for a parameter Z is an interval that is constructed using a method that gives intervals containing the true value of Z, 90% of the time o Suppose (12.2, 17.8) is a 55% confidence interval for μ P(12.2 < μ < 17.8) o Find the CI for EX = μ of a random variable X with a known standard deviation (σ) based on a large random sample of n (n > 30) (1 – α) = 100% CI 90% CI .1 = α If α = .1, then with the formula P(z < z
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Unformatted text preview: .1 ) = 1 = .9 o So z .1 = 1.28 using tables o X-bar = sample mean ~ N(, 2 /n) where is unknown o P( a &lt; xbar &lt; + a) = 1 o P(-a/ xbar &lt; z &lt; a/ xbar ) o a/ xbar = z /2 o a &lt; xbar &lt; + a-xbar a &lt; - &lt; -xbar + a xbar a &lt; &lt; xbar + a o Two sided (1 )100% CI for is (xbar - z / 2 *(/sqrt(n)), xbar + z /2 *(/sqrt(n))) o Lower CI (a, ) o Upper CI (-, b)...
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