Statistic for Business BBUS - Session 7: Sampling, Sampling Distributions and Confidence Interval

Session 7: Sampling, Sampling Distributions and Confidence Interval Statistics for Business Dr. Le Anh Tuan 1 Contents ►Sampling ►Sampling Distribution ►Central Limit Theorem ►Confidence Intervals 2 Sampling 3 Example ► Consider eight random samples of size n = 5 from a large population of GMAT scores (The population parameters are μ = 520.78 and σ = 86.80). ► Sample mean is a statistic ► Sample mean used to estimate population mean is an estimator ! = 504.0 is an estimate ► "1 4 Example ► The sample means have much less variation than the individual sample items. 5 Sampling Distribution ►Sampling distribution is a distribution of all of the possible values of a statistic when a random sample of size n is taken. ►Sampling error is the difference between an estimate and the corresponding population parameter. Example: Sampling error = X - µ ►Bias is the difference between the expected value of the estimator and the true parameter. Example: Bias = E ( X ) - µ 6 Desirable Properties of Estimators ►Unbiased: The expected value of the estimator equal to the parameter being estimated. ►The sample mean is an unbiased estimator of the population mean when E ( X ) = µ ►On average, an unbiased estimator neither overstates nor understates the true parameter. 7 Desirable Properties of Estimators ►Efficiency: ►Refers to the variance of the estimator’s sampling distribution. ►A more efficient estimator has smaller variance. ►Among all unbiased estimators, we prefer the minimum variance estimator. 8