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09_14_09ans - STAT 409 Examples for Fall 2009 1 Suppose the...

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STAT 409 Examples for 09/14/2009 Fall 2009 1. Suppose the lifetime of a particular brand of light bulbs is normally distributed with standard deviation of 75 hours and unknown mean. a) What is the probability that in a random sample of 49 bulbs, the average lifetime X is within 21 hours of the overall average lifetime? σ = 75, n = 49. P( μ – 21 < X < μ + 21 ) = ( 29 ( 29 - + < < - - 49 75 21 Z 49 75 21 P μ μ μ μ = P( 1.96 < Z < 1.96 ) = 0.95 . b) Suppose the sample average lifetime of the 49 bulbs is x = 843 hours. Construct a 95% confidence interval for the overall average lifetime for light bulbs of this brand. ( X – 21, X + 21 ) ( 822 , 864 ) A confidence interval is a range of numbers believed to include an unknown population parameter. Associated with the interval is a measure of the confidence we have that the interval does indeed contain the parameter of interest. A (1 - α ) 100% confidence interval for the population mean μ when σ is known and sampling is done from a normal population, or with a large sample, is
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