Question

Provide an real life example of a confidence interval and how it can be used, listing also advantages and disadvantages associated with it. (In 300 words or more)

Answer 1

A confidence interval is the probability that a value will fall between an upper and lower bound of a probability distribution. The confidence interval can take any number of probabilities, with the most common being 95% or 99%.
confidence intervals is used by Statisticians to measure uncertainty. A higher probability associated with the confidence interval means that there is a greater degree of certainty that the parameter falls within the bounds of the interval. Therefore, a higher confidence level indicates that the parameters must be broader to ensure that level of confidence.

For example, suppose a group of researchers is studying the heights of girls interested in modelling field in high school, The researchers take a random sample from the population and establish a 95% confidence interval using the sample mean the researchers arrive at an upper and lower bound assume the interval is 65 inches to 69 inches which contains the true mean 95% of the time. If the researchers take 100 random samples from the population of girls interested in modelling field in high school as a whole, the mean should fall between 65 and 69 inches in 95 of those samples.

If the researchers want even greater confidence, they can expand the interval to 99% confidence. Doing so invariably creates a broader range, as it makes room for a greater number of sample means. If they establish the 99% confidence interval as 65 inches to 69 inches, they can expect 99 of 100 samples evaluated to contain a mean value between these numbers.

Advantages:

It provides a range of values with known probabilities of capturing the population parameters

It helps one to not be so confident that the population value is exactly equal to the single point estimate.

It makes us more careful in how we interpret our data and helps keep us in proper perspective.

Disadvantage:

The bigger your sample size, the more narrow the confidence interval will be. If you want narrow (i.e., very precise) confidence intervals, then remember to include a lot of participants in your research study.

It requires huge investment of time for sample collecting.