### Sampling Distributions ppt课件介绍及下载

Sampling Distributions ppt课件内容预览：Determine the sampling distributions of:Means.Proportions.Explain the Central LimitTheorem.Determine the effect on the sampling distribution when the samples are relatively large compared to the population from which they are drawn.Sampling Distribution of theMeanWhen the population is normally distributedShape: Regardless of sample size,the distribution of sample means will be normally distributed.Center: The mean of the distribution of sample means is the mean of the population. Sample size does not affect the center of the distribution.Spread: The standard deviation of the distribution of sample means,or the standard error,isStandardizing a Sample Mean on a NormalCurveThe standardized z-score is how far above or below the sample mean is compared to the population mean in units of standard error.“How far above or below”=sample mean minus μ“In units of standard error”=divide byStandardized sample meanCentral LimitTheorempptAccording to the Central Limit Theorem (CLT),the larger the sample size,the more normal the distribution of sample means becomes. The CLT is central to the concept of statistical inference because it permits us to draw conclusions about the population based strictly on sample data without having knowledge about the distribution of the underlying population.Sampling Distribution of theMeanWhen the population is not normally distributedShape: When the sample size taken from such a population is sufficiently large,the distribution of its sample means will be approximately normally distributed regardless of the shape of the underlying population those samples are taken from. According to the Central Limit Theorem,the larger the sample size,the more normal the distribution of sample means becomes.Sampling Distribution of theMeanWhen the population is not normally distributedCenter: The mean of the distribution of sample means is the mean of the population,μ. Sample size does not affect the center of the distribution.Spread: The standard deviation of the distribution of sample means,or the standard error,isExample: Standardizing aMeanProblem 8.45: When a production machine is properly calibrated,it requires an average of 25seconds per unit produced,with a standard deviation of 3seconds. For a simple random sample of n =36units,the sample mean is found to be 26.2seconds per unit. When the machine is properly calibrated,what is the probability that the mean for a simple random sample of this size will be at least 26.2seconds?Standardized sample mean:Sampling Distribution of theProportionWhen the sample statistic is generated by a count not a measurement,the proportion of successes in a sample of n trials is p,whereShape: Whenever both n p and n(1– p)are greater than or equal to 5,the distribution of sample proportions will be approximately normally distributed.Sampling Distribution of theProportionWhen the sample proportion of successes in a sample of n trials is p,Center: The center of the distribution of sample proportions is the center of the population,p.

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