# 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 . What’s the probability distribution of 1 X ? What’s 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 The probability distribution of X A population consists of bottles of shampoo One bottle of shampoo randomly selected and the amount of shampoo measured The random variable X A random sample of n shampoo bottles and n X X X , , , variables random d distribute y identicall and t Independen 2 1
3 The Physical Population consists of bottles of shampoo rolling out from the machine. It has many characteristics that are irrelevant …. The 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 observations collected from the physical population are random variables with probability distributions the same as the statistical population . That is, the random sample X X X n 12 ,, ,  are independent identically distributed random variables having the statistical population as the common distribution. From now on, when talking about the random sample X X X n , , the population means the statistical population . A statistic is a value calculated from the random sample. For example, the sample mean and sample variance are statistics. The probability distribution of a statistic is the sampling distribution of the statistic.

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4 Visualize the sampling distribution: To help you see how a sampling distribution comes about. Consider the sales records of four salespersons last month.
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## This note was uploaded on 02/13/2012 for the course ISOM 111 taught by Professor Hu,inchi during the Fall '10 term at HKUST.

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lct09 - Introduction to Business Statistics Lecture 9...

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