STAT 400 Lecture AL1 1 Examples for 7 1 7 4 Spring 2015 Dalpiaz 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 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 1 100 confidence interval for the population mean when is known and sampling is done from a normal population or with a large sample is X z 2 n X z 2 n X z 2 n estimate margin of error point estimate 1 X z 2 n continued Suppose the sample average lifetime of n 49 bulbs is x 843 hours b Construct a 95 confidence interval for the overall average lifetime for light bulbs of this brand c Construct a 90 confidence interval for the overall average lifetime for light bulbs d Construct a 92 confidence interval for the overall average lifetime for light bulbs Minimum required sample size in estimating the population mean to within with 1 100 confidence is z n 2 2 Always round n up 2 How many test runs of an automobile are required for determining its average miles per gallon rating on the highway to within 0 5 miles per gallon with 95 confidence if a guess is that the variance of the population of miles per gallon is about 6 25 1 continued e What is the minimum sample size required if we wish to estimate the overall average lifetime for light bulbs to within 10 hours with 90 confidence
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