Point Estimates We can estimate a with a Sample Population Parameter... Statistic (a Point Estimate) Mean Proportion p Ps Statistics for Managers Using Microsoft Excel Chap7-6
Statistics for Managers Using Microsoft Excel Chap 7-6 We can estimate a Population Parameter … Point Estimates with a Sample Statistic (a Point Estimate) Mean Proportion p s p μ X
Learning Goals After completing this chapter,you should be able to: >Distinguish between a point estimate and a confidence interval estimate >Construct and interpret a confidence interval estimate for a single population mean using both the Z and t distributions >Form and interpret a confidence interval estimate for a single population proportion >Determine the required sample size to estimate a mean or proportion within a specified margin of error Statistics for Ma agers Using Microsoft Excel Chap7-7
Statistics for Managers Using Microsoft Excel Chap 7-7 Learning Goals After completing this chapter, you should be able to: Distinguish between a point estimate and a confidence interval estimate Construct and interpret a confidence interval estimate for a single population mean using both the Z and t distributions Form and interpret a confidence interval estimate for a single population proportion Determine the required sample size to estimate a mean or proportion within a specified margin of error
Confidence Interval Estimate >An interval gives a range of values: .Takes into consideration variation in sample statistics from sample to sample Based on observation from 1 sample Gives information about closeness to unknown population parameters Stated in terms of level of confidence -Can never be 100%confident Statistics for Mar agers Using Microsoft Excel Chap7-8
Statistics for Managers Using Microsoft Excel Chap 7-8 Confidence Interval Estimate An interval gives a range of values: Takes into consideration variation in sample statistics from sample to sample Based on observation from 1 sample Gives information about closeness to unknown population parameters Stated in terms of level of confidence Can never be 100% confident
Estimation Process Random Sample I am 95% confident that Population μis between Mean 40&60. (meanμ，is X=50 unknown) A 95%confidence interval estimate is Sample interpreted as follows:if all possible samples of the same size n are taken and their sample means are computed, 95%of the intervals include the true population mean somewhere within the interval around their sample means,and only 5%of them do not. Statistics for Ma nagers Using Microsoft Excel Chap 7-9
Statistics for Managers Using Microsoft Excel Chap 7-9 Estimation Process (mean, μ, is unknown) Population Random Sample Mean X = 50 Sample I am 95% confident that μ is between 40 & 60. A 95% confidence interval estimate is interpreted as follows: if all possible samples of the same size n are taken and their sample means are computed, 95% of the intervals include the true population mean somewhere within the interval around their sample means, and only 5% of them do not
General Formula >The general formula for all confidence intervals is: Point Estimate+(Critical Value)(Standard Error) Margin of error (e) Margin of error(e)=(UCL-LCL)/2 Point Estimate =(UCL+LCL)/2 Confidence Interval=2*Margin of error Statistics for Ma Using Microsoft Excel Chap 7-10
Statistics for Managers Using Microsoft Excel Chap 7-10 General Formula The general formula for all confidence intervals is: Point Estimate ± (Critical Value)(Standard Error) Margin of error (e) Margin of error (e)=(UCL-LCL)/2 Point Estimate = (UCL+LCL)/2 Confidence Interval=2*Margin of error