10_27_1 - STAT 400 1. Examples for 10/27/2011 (1) Fall 2011...

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STAT 400 Examples for 10/27/2011 (1) Fall 2011 1. Suppose the lifetime of a particular brand of light bulbs is normally distributed with standard deviation of σ = 75 hours and unknown mean. a) What is the probability that in a random sample of n = 49 bulbs, the average lifetime X is within 21 hours of the overall average lifetime? b) Suppose the sample average lifetime of n = 49 bulbs is x = 843 hours. Construct a 95% confidence interval for the overall average lifetime for light bulbs of this brand. 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 α + α - σ σ n z n z , 2 2 X X
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X ± n z σ α 2 X ± ε estimate
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10_27_1 - STAT 400 1. Examples for 10/27/2011 (1) Fall 2011...

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