AF SEctions 6.4-6.6 handouts

# AF SEctions 6.4-6.6 handouts - STAT 2000 Sections 6.4-6.6...

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10/15/2008 1 STAT 2000 Sections 6.4-6.6 Sampling Distributions Agresti-Franklin Sampling Distributions •What other distributions have we talked about? •How do we describe distributions? A sampling distribution is a probability distribution for a statistic. It provides probabilities for the possible values of the statistic. Statistics we have studied: , s Sampling Distribution of the Sample Mean, Section 6.5 - first Sampling Distribution of the Sample Proportion x x Section 6.4 - second We will determine shape, center and spread for each of these sampling distributions. We will also use these distributions to find probabilities. Why are sampling distributions important? Regulating Nicotine in Cigarettes The conditions prescribed in the FTC's 1967 announcement are the following: 1. Smoke cigarettes to a 23mm. butt length, or to the length of the filter and overwrap plus 3mm. if in excess of 23mm.; 2 Base results on a test of 100 cigarettes per 2. Base results on a test of 100 cigarettes per brand, or type; 3. Cigarettes to be tested will be selected on a random basis, as opposed to "weight selection"; Report nicotine yield to the nearest 1/10 milligram. Tar yield and CO concentration are also reported. If one cigarette had been tested, and the population was normal, we could find the probability that the nicotine content of that cigarette was more than 1.72 milligrams (the yield in 1998). Note, however, that 100 cigarettes are tested. In this case, the average is calculated, and we want to find the probability that the SAMPLE AVERAGE, , is more than 1.72 milligrams. In order to find this probability, we will have to know more about the distribution of the sample averages, the sampling distribution of the sample mean. x Class Exercise: Working in pairs, toss a die 4 times. Record the number of dots and calculate the average.

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10/15/2008 2 We will look at the THREE different distributions that are part of this exercise. Population Distribution : The distribution from which we took our sample. Data Distribution : The distribution of the data from ONE sample. Sampling Distribution of the Sample Mean: The distribution of the sample averages. Population Distribution | | 1/6 | | | |_______________________________ X 123456 Shape: Center: Spread: Data Distribution - One Sample | | | | | | x |_______________________________ Shape: Center: Spread: Sampling Distribution: Distribution of values | | | | | | x _______________________________ 1 2 3 4 5 6 x Shape: Center: Spread: Sampling Distribution of the Sample Mean Center : The mean of the sampling distribution of equals the mean of the population.
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AF SEctions 6.4-6.6 handouts - STAT 2000 Sections 6.4-6.6...

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