学习大二下南新statistics for business11for ln ch10statistical inference about means and proportions with two populations.pptxVIP

中山大学岭南学院教授 夏南新博士 制作;11.1 ESTIMATION OF DIFFERENCE BETWEEN THE  MEANS OF TWO POPULATIONS:  INDEPENDENT SAMPLES; As with other point estimator, the point estimator has a standard error that des-cribes the variation in the sampling distribut-ion of the estimator. With two independent simple random samples, the standard error of is as follows: Where point estimator= ;Standard Error: where standard deviation of population 1 standard deviation of population 2 sample size for the simple random sample from population 1 sample size for the simple random sample from population 2;If both populations have a normal distributi-on, or if the sample size are large enough th-at the central limit theorem enables us to co-nclude that the sampling distribution of and can be approximated by a normal dis-tribution, the sampling distribution of will have a normal distribution with mean given by . A point estimator a margin of error Margin of error;Interval Estimate of : Large-Sample Case ;When the population standard deviations are unknown, we can use the sample stan-dard deviations as estimates of the popul-ation standard deviations and estimate as follows. Point Estimator of ;;Thus, in the large-sample case, we can use the point estimator of to develop the following confidence interval estimate of the difference between the two population means. Interval Estimate of the Difference Betw-een the Means of Two Populations: Large-Sample Case ( and ) with and Estimated by and where is the confidence coefficient ;Interval Estimate of : Small-Sample Case When and are estimated by and , the distribution is used to develop the small-sample interval estimate