Central Limit Theorem and Statistical Inferences

CLT is significant because the results hold regardless of what shape the original population distribution was, which makes it important for statistical inference. The more data that's gathered, the more accurate the statistical inferences become, meaning more certainty in estimates.

Central Limit Theorem and Inferential Statistics

Inferential statistics uses sample data to make reasonable judgments about the population where data originated. It's used to examine relationships between variables within a sample and make predictions about how the variables will relate to a larger population.

Inferential statistics are particularly useful because it's difficult (and in some cases, impossible), expensive, and time-consuming to study an entire population of people. But by utilizing a statistically valid sample and inferential statistics, a data scientist can perform research that produces accurate results.

Some techniques that are used in inferential statistics include:

Business Utilization of Central Limit Theorem and Statistical Inferences

Usually, businesses measure financial holdings regarding the end benefit. However, as there is risk associated with these financial holdings, central limit theorem helps in giving a clear picture of the risk involved versus the benefits. This inference is drawn based on the pattern from the normal distribution and utilizing the central limit theorem. Businesses analyze such situations by collating the trend reports regarding how individual contributors to the business have performed during the past business cycles and put that information into an investment model. As the returns from the contributors vary, the associated mean value for each is calculated based on taking several sets of samples reflecting the performance of each contributor.

With this, two key statistical inference can be drawn – one is the approximate average return from each contributor and the normal distribution of the sample averages. This information provides the information regarding how much risk is associated with each contributor to take appropriate decisions.

The CLT provides results that indicate that for a large enough sample size, the distribution of X becomes closer to normal regardless of what the underlined distribution of X is. Basically, this means that no matter the circumstance, it's possible to make probabilistic inferences about population parameter values based on statistic samples.

Example of a Retail Company

A retail company has a contract for their employees working in product manufacturing and distribution which says that they receive bonus pay if they can produce at least 100 products per day that are free of defects.

The CLT means that if the portfolio contains enough stocks, the return will be normally distributed, meaning E (R) and variance V (R).