第八章样本分布.ppt

CHAPTER 8: Sampling Distributions to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel ? 2002 The Wadsworth Group Chapter 8 - Learning Objectives Determine the sampling distributions of: Means. Proportions. Explain the Central Limit Theorem. Determine the effect on the sampling distribution when the samples are relatively large compared to the population from which they are drawn. Sampling Distribution of the Mean When the population is normally distributed Shape: Regardless of sample size, the distribution of sample means will be normally distributed. Center: The mean of the distribution of sample means is the mean of the population. Sample size does not affect the center of the distribution. Spread: The standard deviation of the distribution of sample means, or the standard error, is Standardizing a Sample Mean on a Normal Curve The standardized z-score is how far above or below the sample mean is compared to the population mean in units of standard error. “How far above or below” = sample mean minus μ “In units of standard error” = divide by Standardized sample mean Central Limit Theorem According to the Central Limit Theorem (CLT), the larger the sample size, the more normal the distribution of sample means becomes. The CLT is central to the concept of statistical inference because it permits us to draw conclusions about the population based strictly on sample data without having knowledge about the distribution of the underlying population. Sampling Distribution of the Mean When the population is not normally distributed Shape: When the sample size taken from such a population is sufficiently large, the distribution of its sample means will be approximately normally distributed regardless of the shape of the underlying population those samples are taken from. According to the Central Limit Theorem, the larger the sample size, the more no