Lecture8-1

# Lecture8-1 - BUAD 310 Applied Business Statistics Quiz 2...

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BUAD 310 Applied Business Statistics Quiz 2 Review 3/1/10

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CI for a Population Mean 2 A confidence interval for an unknown population mean has the form Margin of error is a multiple of the SD or SE of the sample mean. Recall that deviation. standard sample the is and deviation population is where s n s x SE n x SD ) ( ) ( error of margin x
CI for a Population Mean with Known σ 3 If sampled population has mean μ and known σ, a (1-α)100% confidence interval for μ is /2 xz n 1.645 1.960 2.576 Level 90% 95% 99% 2 / z E.g.,

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Effect of Confidence Level on CI Width 4 The higher the confidence level (1-α)100% (e.g., 99%>95%), the longer is the CI.
CI for a Population Mean with Unknown σ 5 If sampled population is normally distributed with mean and unknown σ, then a (1 - α)100% confidence interval for μ is /2 s xt n is the t point giving right-hand tail area of /2 under t curve having n – 1 degrees of freedom (df). t

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Effect of df on t Distribution 6 As the number of degrees of freedom (df) increases, spread of t distribution decreases and the t curve approaches the standard normal curve. df =
More Practice 7 A business magazine samples 90 individuals responsible for economic forecasting for regional banks. Suppose that the sample of 90 forecasts yields an average prediction of a 2.7% growth in real disposable income. Assume that the population standard deviation is 0.4%. Calculate a 95% confidence interval for the population mean forecast.   783 . 2 , 617 . 2 083 . 0 7 . 2 90 4 . 0 96 . 1 7 . 2 025 . n z x 246 take 9 . 245 05 . 0 4 . 0 96 . 1 4 . 0 96 . 1 05 . 0 0.05? to 0.083 from error of margin lower the we could How 2 n n n

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More Practice 8 An airline needs an estimate of the average number of passengers on a newly scheduled flight. The mean of a sample of 30 days is found to be 112.0 and the sample standard deviation is 25. Find a 95% confidence interval for the true mean.   334 . 121 , 666 . 102 334 . 9 112 30 25 045 . 2 112 025 . n s t x 29 30 df n
More Practice 9 An airline has 4 ticket counter positions at a particular airport. In an attempt to reduce waiting lines for customers, the airline introduces the “snake system.” Under this system, all customers enter a single waiting line that winds back and forth in front of the counter. A customer who reaches the front of the line proceeds to the first free position. The manager measures the waiting time for a sample of 15 customers and finds the mean time of 5.043 minutes and standard deviation of 2.266. Calculate a 95% CI for the mean waiting time under the new system.   298 . 6 , 788 . 3 255 . 1 043 . 5 15 266 . 2 145 . 2 043 . 5 14 15 025 . n s t x df n How about a 90% CI?   073 . 6 , 013 . 4 030 . 1 043 . 5 15 266 . 2 761 . 1 043 . 5 050 . n s t x

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CI for a Population Proportion 10 A confidence interval for an unknown population proportion p has the form Margin of error is a multiple of the SE of the sample proportion . p ˆ error of margin p ˆ
CI for a Population Proportion 11 A (1 - α)100% confidence interval for population proportion

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Lecture8-1 - BUAD 310 Applied Business Statistics Quiz 2...

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