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### Sampling Distributions and Confidence Intervals

**ORDER INSTRUCTIONS:**

1. What is the central limit theorem? What role does it play in the establishment of the sampling distribution of the sample mean?

2. Contrast normal distributions with sampling distributions.

In statistical inference, one wishes to estimate population parameters using observed sample data.

A ** confidence interval** gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. (

*Definition taken from Valerie J. Easton and John H. McColl’s Statistics Glossary v1.1*)

The common notation for the parameter in question is . Often, this parameter is the population mean , which is estimated through the sample mean .

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#### Sampling Distributions and Confidence Intervals Essay

**The central limit theorem**

The central limit theorem refers to a theory in probability statistics where the approach is that the distributions of a normalized….

**The role of the Central Limit Theorem in the establishment of the sampling distributions of the sample mean**

A major role of the central Limit theorem in terms of establishing sampling distributions is the use of inference from the available….

**Contrasting normal distributions with sampling distributions**

Normal distributions refer to a normal continuous probability distribution that when….

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