# [SOLVED] Wk 3 DiscussionCentral Limit Theorem

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Review Chapter 8. Consider the concept of point estimate and discuss the need to build a confidence interval using the point estimate.

Consider the phrase “confidence interval” – what does the word “confidence” imply and what is the information provided by the word “interval”?

Provide an example to illustrate the concepts.

By Alycia

The central limit theorem is the idea that the sampling distribution of the mean of any independent and random variable will be normal or close to normal if the sample size is large enough.

To answer the question of how large is large enough when taking a sample two factors should be considered:

1. The requirements of accuracy, more sample points will be required depending on the more closely the sampling distribution needs to resemble a normal distribution.
2. The shape of the underlying population. Fewer sample points are needed the more closely the original population resembles a normal distribution.

If the original population and information is distinctly not normal because it’s badly skewed, has more than one peak, and/or has outliers, then the sample size should be larger than the standard recommendation of 30-40 for a population distribution that is nearly normal and bell shaped.

https://stattrek.com/statistics/dictionary.aspx?definition=sampling_distribution

By Debra

A sampling error occurs when the data selected does correctly the entire population which the results would have turned out differently. Sampling error information can skewed or bias based on the data set chosen. For example if a company was doing a survey for products that are only used by a few people or only a few people respond the information may not be reflection of how well the company products sale.

Sampling Distribution of Sample Means basically states that as sampling increases the relative distribution becomes closer. For example, if you use 100 samples is fairly close but 100,000 samples will be even closer.

Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger regardless of the population distribution shape.

Standard Error of the Mean when using a larger sampling size for example using a wider demographic or city to calculate income or poverty levels you will better understand the standard deviations. The smaller the error the better the population will be represented.

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