Confidence Intervals

Understanding confidence intervals (population parameters- mean and variance, point estimates- proportions)

A confidence interval is a representation of the probability that a certain population estimate will be between a certain set of values for a certain proportion of the time. In simpler terms, a confidence interval is the range of values what we are are sure the true value will lie at a given proportions mostly expressed as a percentage. The key highlights bout confidence intervals are;

1. A confidence interval will show the chance that a certain population parameter will be between a certain range of values.
2. Confidence intervals are a measure of uncertainty or the certainty in sampling and sampling distributions.
3. The amount of certainty or uncertainty in confidence intervals is measured in percentage of a proportions called confidence levels. They will often be made using confidence levels of 95% or 99%.

The confidence interval is used by statisticians and researchers to help them understand their samples and identify the uncertainty their samples bring in to their evaluations. When a researcher is using a certain sampling procedure, they might decide to take different samples from the populations and cerate confidence intervals for each of the samples. Using the calculated confidence intervals, the researchers will be in a position to know how the samples are a representation of the true value of the population under investigation. As a result, a researcher will be able to select a sample that is a true representation of the population to make accurate findings from the data.
To get a better understanding of the confidence interval, let us use an example about the average height of the average American. Since it will be impossible to collect the height of each and every American, a searcher will use a sample size, by taking maybe 200 American at random and measuring their height, the researcher might calculate the mean height of the sample of 200 American. And because we do not have the true value height of American, a confidence interval from the sample size will be used to tell us how close or far away, the average height of 200 Americans is from the actually average height of all Americans. For instance, if the 95% confidence interval of the mean height of the sample was between 65 and 70 inches, we can be 95% confident that the average height of all Americans (the entire population) is between 65 inches and 70 inches tall. This example is a good explanation to help you understand the confidence interval.

Various misconceptions have been said about the confidence intervals, one of the most stated misconception is the interpretation of the confidence intervals. The misconception assumes that the confidence interval is a percentage of data observation in a sample that fall between a certain range of values. For example, if the 95% confidence intervals of the sample mean has been calculated to maybe 65 to 70 meters, one can wrongly state that 95% of the data will fall between 65 and 70 meters, however, the correct interpretation should be that, we are 95% confident that the average population parameter will be between these two ranges know as a lower and an upper bound.

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