Central Limit Theorem in Statistical Analysis Paper Example

Statistical analysis is one of the components in data analysis. As a science, it deals with identifying patterns and trends after data has been collected. Collection of data is always followed by clear and detailed scrutiny for analysis. To do this, statisticians employ different tools and approaches to make sure that data has been analyzed clearly. One of the approaches in data analysis is by the use of the central limit theorem. The theorem states that if there is a population under analysis with a known mean and standard deviation, the distribution of the means in the sample will be approximately normally distributed. This is the case if large random samples are taken with replacement in the population ("Theorem | STAT 414 / 415," n.d.). In statistical analysis, the central limit theorem is important as it helps in testing claims and calculating a probability.

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The most commonly use of the Central Limit Theorem is testing a claim in statistical analysis. The theorem states that the sample mean should be normally distributed with the mean in the population. With this in mind, we can test a claim by identifying if the probability of a claim made on the population can obtain a sample mean as large as the one already identified. If so, the claim is right and if not so, the claim is wrong. In this way, the central limit theorem also helps in testing hypotheses (claims) made about sample means ("Central Limit Theorem," n.d.). Additionally, the Central limit theorem can also be used to test the probability that a sample mean falls with a certain range. To get this, a standard normal is drawn and using it, the probability in percentage is established ("Theorem | STAT 414 / 415," n.d.). An example of such a task is when testing the probability that the mean of a sample will fall under a certain range of values.

An increase in the number of samples and a similar increase in the number of data in each sample will significantly affect the distribution mean and the standard deviation. The distribution means remains the same with an increase in the sample ("Sampling Distribution and Central Limit Theorem," n.d.). However, the standard deviation decreases with an increase in the sample. In a nutshell, an increase in the sample size results to decrease in the standard deviation while a decrease in the sample results to an increase in the standard deviation.

The use of the central limit theorem relates closely but not directly to simulation modelling. In simulation modelling, one assumes to be working with a real thing while working with imitations. The use of simulation models is used in a variety of fields. The relationship between the simulation models and the central limit theorem is that in both, there is the technique of testing hypotheses (Claims) before decisions are made ("Modeling and Simulation," n.d.). While the use of central limit theorem uses statistical calculations by drawing a standard deviation graph, simulation models use imitations.

Conclusion

In conclusion, the use of the central limit theorem is a widely used approach in statistical analysis. It is an important technique as it helps in identifying probabilities and also used in testing claims. The theory is closed related to simulation modelling as both are used to test hypothesis though by use of different approaches.

References

Central Limit Theorem. (n.d.). Retrieved from http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Probability/BS704_Probability12.html Accessed 3rd November 2018.

Modelling and Simulation. (n.d.). Retrieved from http://home.ubalt.edu/ntsbarsh/Business-stat/simulation/sim.htm#rwis Accessed 3rd November 2018.

Sampling Distribution and Central Limit Theorem. (n.d.). Retrieved from http://srjcstaff.santarosa.edu/~ylin/Math15/notes/Sampling_Distribution_CLT.htm Accessed 3rd November 2018.

The Theorem | STAT 414 / 415. (n.d.). Retrieved from https://onlinecourses.science.psu.edu/stat414/node/176/ Accessed 3rd November 2018.