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Unformatted text preview: 1 Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 1 Business Statistics II ECO 362: Sections A & B Review of Chapters 8, 9, & 10 Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 2 Chapter 8: Interval Estimation s Population Mean: σ Known s Population Mean: σ Unknown s Population Proportion Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 3 Margin of Error s Interval estimate: add and subtract a margin of error to the point estimate. Point Estimate +/ Margin of Error s Interval estimate of a population mean ̅x̅ +/ Margin of Error s Interval estimate of a population proportion ̅p̅ +/ Margin of Error Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 4 μ α /2 α /2 α /2 α /2 1  α of all values 1  α of all values x x z x α σ /2 z x α σ /2 Interval Estimation of a Population Mean: σ Known Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 5 x z n ± α σ /2 where: is the sample mean 1  α is the confidence coefficient α is the level of significance z α /2 is the z value providing an area of α /2 in the upper tail of the standard normal probability distribution σ is the population standard deviation n is the sample size x Interval Estimation of a Population Mean: σ Known s Interval estimate of µ Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 6 Example: Discount Sounds s 260 retail outlets throughout the US. s Potential location for a new outlet based on the mean annual income. s A sample of size n = 36 was taken. s The sample mean income is $31,100. s The population is not highly skewed. s The population standard deviation is $4,500. s The confidence coefficient to be used in the interval estimate is .95. 2 Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 7 95% of the sample means that can be observed are within + 1.96 of the population mean μ . σ x The margin of error is: α σ = = /2 4,500 1.96 1,470 36 z n Thus, at 95% confidence, the margin of error is $1,470. Example: Discount Sounds Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 8 Interval estimate of μ is: We are 95% confident that the interval contains the population mean. $31,100 + $1,470 or $29,630 to $32,570 Example: Discount Sounds Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 9 s Interval Estimate x t s n ± α /2 where: 1  α = the confidence coefficient t α /2 /2 = the t value providing an area of α /2 in the upper tail of a t distribution with n 1 degrees of freedom s = the sample standard deviation Interval Estimation of a Population Mean: σ Unknown Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 10 Example: Apartment Rents s A reporter for a student newspaper is...
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 Spring '11
 
 Normal Distribution, Plattsburgh, SUNY Plattsburgh, School of Business and Economics, Dr. Kameliia Petrova

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