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7.2 - The Mean and Standard Deviation of The relation = *** See example 7.4, p. 319 Mean of the variable For samples of size n, the mean of all possible sample means equal the mean of the population. = The relation between and *** See example 7.5, p. 320 Standard Deviation of the Variable For samples of size n, the standard deviation of all possible sample means equals the population standard deviation divided by the square root of the sample size. = n Note When sampling is done without replacement from a finite population the approximate formula is N n = N 1 n where n is the sample size and N is the population size. When the sample size is small relative to the population size (that is, n 0.05N), as happens in most practical applications, there is little difference between sampling with and without replacement and the answers from the two formulas are “close”. In this book we’ll be using the first formula with the understanding that the answers may be only approximate. *** See example 7.6, p. 322 *** do # 7.30, p. 324 *** do # 7.32, p. 324 *** do # 7.34, p. 324 Standard Error (SE) of the Sample Mean: The standard deviation of determines the amount of sampling error to be expected when a population mean is estimated by a sample mean. This sampling error gets smaller as the sample size increases. ▪ The larger the sample size, the smaller is the standard deviation of . ▪ The smaller the standard deviation of , the more closely the possible values of cluster around the mean of .