Simulation – Output Analysis

Point Estimate Point estimates are single value estimates of parameters of interest (in this case the mean and standard deviation of the population) Point estimates are single value estimates of parameters of interest (in this case the mean and standard deviation of the population) Point estimates are calculated for the mean (μ) and standard deviation (σ) of the population from sample values Point estimates are calculated for the mean (μ) and standard deviation (σ) of the population from sample values –Estimate of μ: n = sample size (number of observations) x i = value of the ith observation –Estimate of σ: –Sample variance s 2 is used to estimate the variance of the population σ 2

Determining point estimates Buddy’s Style Shop (pg 225) Buddy’s Style Shop (pg 225) and s will have different values if based on another set of independent observations and s will have different values if based on another set of independent observations

Interval estimates A point estimate, by itself, gives little information about how accurately it estimates the true value of the unknown parameter A point estimate, by itself, gives little information about how accurately it estimates the true value of the unknown parameter An interval estimate provides info on how far off the point estimate might be from the true value of the unknown parameter – confidence interval estimation An interval estimate provides info on how far off the point estimate might be from the true value of the unknown parameter – confidence interval estimation

Confidence interval A range within which one can have a certain level of confidence that the true but unknown mean falls A range within which one can have a certain level of confidence that the true but unknown mean falls The interval is symmetric about and the distance that each endpoint is from is called the half-width (hw) The interval is symmetric about and the distance that each endpoint is from is called the half-width (hw) The confidence interval is expressed as the probability P that the unknown true mean μ lies within the interval The confidence interval is expressed as the probability P that the unknown true mean μ lies within the interval

Calculating the half-width t n-1,α/2 = obtained from Student’s t table in Appendix B (pg 724) n-1 = degrees of freedom (df) α = 1-P = significance level Buddy’s Style Shop (pg 227) Buddy’s Style Shop (pg 227) Fantastic Dan example (use Sheet Properties) Fantastic Dan example (use Sheet Properties)