What do confidence intervals represent? What is the most controllable method of increasing the precision of or narrowing the confidence interval? What percentage of times will the mean, or population proportion, not be found within the confidence interval?

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A confidence interval for the mean is a range ìlower < ì <ìupper where the lower bound is the smallest value of ì that we expect and the upper bound is the largest value of ì that we expect”(Doane-Seward,2007).

“If we wanted a narrower interval(i.e. more precision) we could either increase the sample size or lower the confidence level.”
5% the mean(population proportion) will not be found within the confidence interval.

Confidence intervals represent a range of values within which the true value of a parameter is likely to fall. They are commonly used in statistics to estimate population parameters, such as the population mean or proportion, based on sample data.

To increase the precision or narrow the confidence interval, you can do the following:

1. Increase the sample size: Increasing the sample size allows for more information to be collected and reduces the variability in the estimates. A larger sample size generally leads to a smaller margin of error and a narrower confidence interval.

2. Decrease the confidence level: The confidence level is the degree of certainty that the true population parameter falls within the calculated interval. By reducing the confidence level (e.g., from 95% to 90%), the margin of error decreases, resulting in a narrower confidence interval. However, this also increases the risk of capturing an incorrect value.

It's important to note that increasing the precision or narrowing the confidence interval often requires a trade-off with other considerations, such as time, cost, and practicality.

Regarding the percentage of times the mean or population proportion will not be found within the confidence interval, it depends on the confidence level chosen. By convention, a confidence level of 95% is commonly used, which means that in the long run, 95% of confidence intervals constructed using the same method will contain the true population parameter, while 5% will not. Similarly, with a 90% confidence level, 90% of intervals will contain the parameter, while 10% will not.