lct09 - Introduction to Business Statistics Lecture 9...

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1 Introduction to Business Statistics Lecture 9 Sampling Distributions Example 1. A machine is designed to fill each empty bottle with 300 gram of shampoo. However, the actual amount of shampoo poured into the bottle is random, which varies from bottle to bottle. Suppose we suspected that the machine is out of control and the mean is greater than 300 g. To answer the question, we take a sample X X X n 12 ,, , ⋅⋅⋅ of size n and calculate the sample mean, n X X X X n / ) ( 2 1 + + = . z What is the probability distribution of 1 X and what is its relationship with the population? (If 2 . 0 ) 305 300 ( 1 = < < X P , say, then what is the proportion of bottles from the machine having between 300 g and 305 g of shampoo?)
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2 Physical Population consists of bottles of shampoo rolling out from the machine. It has many characteristics that are irrelevant …. Statistical Population is the probability distribution of the random amount of shampoo poured into the bottle. It has all the relevant information to answer the question ‘is the machine in or out of control?’ The sample of observations collected from the physical population can be viewed as random variables with probability distributions the same as the statistical population . That is, X X X n 12 ,, , ⋅⋅⋅ are independent random variables having the statistical population as the common distribution. From now on, when talking about the sample X X X n , , the population means the statistical population .
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3 Visualize the sampling distribution: To help you see how a sampling distribution comes about. Consider the sales records of four salespersons last month. Salesperson Units Sold Ann 3 Bob 2 Cathy 1 Dave 4 Suppose we take a sample of size two with replacement, and consider all possible samples of two. The physical population consists of the four salespersons, whereas the statistical population is the probability distribution which puts probability 1/4 on each of the four values 1,2,3,4.
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4 Sample Salespersons
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This note was uploaded on 11/23/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.

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lct09 - Introduction to Business Statistics Lecture 9...

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