2 7 SAMPLING DISTRIBUTION STUDY UNIT 7 Key questions for this unit What is the sampling distribution of the sample mean? What is the sampling distribution of the sample proportion? What is the standard error of the sample mean? What is the standard error of the sample proportion? In many real life applications, you make inferences that are based on statistics calculated from a sample to estimate values of population parameters. In this study unit, we learn about how the sample mean (a statistic) is used to estimate the population mean (a parameter), and how the sample proportion (a statistic) is used to estimate the population proportion (a parameter). Our main focus when making statistical inference is drawing conclusion about a population and not about a sample, hence sampling distribution. A sampling distribution is the distribution of the results if you actually selected all possible samples. The following is the mind map of this study unit. 7.1 Sampling distribution of the sample mean The sampling distribution of the sample mean is the distribution of all possible sample means if you selected all possible samples of a given size. This distribution follows a normal distribution with mean µ = ) ( x E and the standard deviation of the sample mean (the standard error) is n x σ = where is the population standard deviation and n is the
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