Statistical Inference and the Central Limit Theorem

A population parameter is the value of a factor in the target population. While a sample statistic is any summary measure from your collected data such as mean, correlation coefficients, ratios between means, etc.

There is a way to determine the distribution of any given statistic through a computer simulation. An example of a computer simulation to determine the number of heads in 40000 100-coin-tosses would go as follows:

Step 0: Repeat Steps from 1 to 3 40000 times

Step 1: Take a coin and randomly flip it 100 times

Step 2: Count the number of heads

Step 3: Store the number

The plot would be likely to be normally distributed with the mean oscillating between 40 and 60 heads during a 100 coin-toss.

The Central Limit Theorem states that if all possible random samples of the same size S are taken from a population with a given mean and a particular standard deviation, the sampling distribution will have a mean equal to the population mean and the standard deviation of the sampling distribution will be the population SD divided by the square root of S. The CLT also states that the sampling distribution will be approximately normally distributed.

Summary of Hypothesis Testing(enhanced)

  • Define null and alternative hypotheses
  • Compute a null distribution (this would show us what would happen if we randomly collected data and the null hypothesis was true)
  • Collect empirical data
  • Calculate the p value of the empirical data
  • Reject or accept the hypothesis
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One thought on “Statistical Inference and the Central Limit Theorem

  1. […] So plotting the sample means of our samples gives us the sampling distribution of the mean. Click here to see how to compute the sampling distribution of the […]

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