Inferential Statistics and Weird Attributes about Confidence Intervals

Marbles

Inferential Statistics and A BAG OF MARBLES

In its simplest form, inferential statistics is like sticking your hand into a bag with 95 white marbles and 5 black marbles and figuring out the odds that you'll pick a black marble. In another hub, I begin writing about confidence intervals, which are an important application of statistics and accompanied research.

Unusual Attribute about a Confidence Interval

On the other hand, there is another unusual attribute about a confidence interval; meaning there are many different things that can be in a distribution: humans, apples, textbooks, pens, birds, jeans, weight, height, length, or just about anything you can imagine.

But, none of those things can be in the distribution from which a confidence interval is the consequent. There is a little special something and atypical about what can be in a distribution from which a confidence interval is drawn, such as below.

Help with Confidence Intervals. Stats II Really Taught Me A LOT!

Ideas About What is Unusual About this Distribution

  • If a mean in a sample is 0 and the standard deviation is 1, the mean and standard deviation of a population is unknown.
  • To draw confidence intervals to estimate the mean of an unknown population, we use the Central Limit Theorem to estimate the means of all random samples and their distribution within a population.
  • The Central Limit Theorem calculates the means of all samples distributed in a population.
  • If a population is normally distributed, then the sample is normally distributed.
  • If the population is not normal, the sample distribution of the mean will become normally distributed when the sample size grows larger.
  • The Central Limit Theorem is a manner to determine Standard Normal Distribution and Variance in a population of random samples in the distribution of “humans, apples, textbooks, pens, birds, jeans, weight, height, length, or just about anything you can imagine."

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