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Finance & Accounting
Pages 8 (2008 words)
Finance and Accounting Name Institution Introduction Basing on the principle of the central limit theorem, a sampling distribution of statistics becomes normal or near to being normal whenever the sampling size is large enough. When applying this principle for a sampling distribution of the mean, it is possible to find the sample distribution of the means by supposing that if one draws all possible samples of say size n from a given population of say size N, and supposes the mean score for the samples is computed separately, then the sample distribution of the means can be obtained.
x = ? and ?x = ? * sqrt(1/n - 1/N ) Basing on the mathematical expressions above, it is possible to specify the sampling distribution of the mean unless two conditions are met. First, when the population is said to be normally distributed or otherwise if the sample size is said to be sufficiently large. Secondly, the standard population of the population is known. In this problem, the two conditions are met and, therefore, given the standard deviations, and the means of the five samples given, the mean of the population can be calculated through averaging the sample means. This can be accomplished mathematically, as the population mean = (80934 + 78110.48 + 80,340 + 84716.5)/5 = 64,890.196 $. In a sampling distribution of means, the populations mean (?) has been found to always equal to the sampling distribution (?x) mean. ...
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