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PROBABILITY AND STATISTICS

PROBABILITY AND STATISTICS. WEEK 9. The sampling distribution of the sample statistics. The sampling distribution of the sample statistics. C onsider a population of N elements from which we can obtain the following distinct data: { 0 , 2 , 4 , 6 , 8 } .

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PROBABILITY AND STATISTICS

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  1. PROBABILITY AND STATISTICS WEEK 9 Onur Doğan 2016-2017

  2. The sampling distribution of the sample statistics Onur Doğan 2016-2017

  3. The sampling distribution of the sample statistics Consider a population of N elements from which we can obtain thefollowing distinct data: {0, 2, 4, 6, 8}. • Form samples of size 2 for this population. • Define theirmeansandfigurethe bar chart of themeans. • Define the sampling distribution of the sample rangesandfigure bar chart. Onur Doğan 2016-2017

  4. The Central Limit Theorem The mean is the most commonly used sample statistic and thus it is very important.The central limit theorem is about the sampling distribution of sample means of random samplesof size n. Let us establish what we are interested in when studying thisdistribution: 1) Where is the center? 2) How wide is the dispersion? 3) What are the characteristics of the distribution? The central limit theorem gives us an answer to all these questions. Onur Doğan 2016-2017

  5. The Central Limit Theorem Let µbe the mean andσ the standard deviation of a population variable. If we consider allpossible random sample of size n taken from this population, the samplingdistribution of samplemeans will have the following properties: c) if the population is normally distributed the sampling distribution of the samplemeans is normal; if the population is not normally distributed, the samplingdistribution of the sample means is approximately normal for samples of size 30 or more.The approximation to the normal distribution improves with samples of larger size. Onur Doğan 2016-2017

  6. The Central Limit Theorem Onur Doğan 2016-2017

  7. The Central Limit Theorem Onur Doğan 2016-2017

  8. The Central Limit Theorem Onur Doğan 2016-2017

  9. Example Consider a normal population with µ=100 and σ=25. If we choose arandom sample of size n = 36, what is the probability that the mean value of this sample isbetween 90 and 110? In other words, what is P(90 < x < 110)? Onur Doğan 2016-2017

  10. Example Theaveragemaledrinks 2L of waterwhenactiveoutdoor s(withstandarddeviation of 0,7 L). Youareplanning a fulldaynaturetripfor 50 men andbring 110 L of water. What is theprobabilitythatyouwillrunout? Onur Doğan 2016-2017

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