CH5INTRODUCTION TO INFERENTIAL STATISTICS(商务统计,英文版).ppt

Business StatisticsBEO 1106;INTRODUCTION TO INFERENTIAL STATISTICS;Ex 1: Suppose we are interested in the following population: X = {1,2,3,4,5).;;Repeat part b assuming this time that sampling is without replacement.;Compare the X, X-bar1 and X-bar2 populations to each other.;Apart from their means and variances, the X-bar1 and X-bar2 populations can also be characterized by their shapes. ; How to take a sample? ;Random samples can be drawn in several different ways. The most basic procedure is called simple random sampling.;When the population is large, sampling is more complicated. In general, we need ;Sampling error:;This example suggests that;The results from Ex 1 can be generalized as follows.;As for the shape of the sampling distribution of the sample mean, it depends on the distribution of the sampled population and on the sample size.;Ex 2: (Selvanathan, p.285, ex.7.22 (2000 edition – p.237, ex. 7.22)) An automatic machine in a manufacturing process is operating properly if the lengths of an import sub-component are normally distributed, with mean μ = 117 cm and standard deviation σ = 2.1 cm.;Ex 3: Imagine we have a large population of, say, invoices with μ = $255.60 and σ = $45.20.;and; Let us suppose that a population has only two types of elements (such as yes – no, female – male, defective – non-defective etc.), ;and it can be shown, that ;Population; There is, however, an important difference: a binary population cannot be normally distributed, so p-hat is not normally distributed either.;Ex 4: From past experience 10% of electronic components received from a particular manufacturer are defective. If, from a particular shipment, a random sample of 400 components is selected, what is the probability that the proportion of defective parts in the sample is;less than 9%?