One can calculate the 95% confidence interval for the mean with the population standard deviation known. This will give us an upper and a lower confidence limit. What happens if we decide to calculate the 99% confidence interval? Describe how the increase in the confidence level has changed the width of the confidence interval. Do the same for the confidence interval set at 80%. Include an example with actual numerical values for the intervals in your post to help with your explanations.

~ Confidence Intervals

While not overly detailed, the link below describes in general terms what a “confidence interval” really is and why we use it. Check out the description of confidence interval from the NIST Engineering Statistics Handbook link to see if it makes sense to you. This is a resource used by scientists and engineers and so provides practical applications for statistics outside of business.

A very common confidence interval in academic research is 95%. In a different textbook than the one we’re using, the authors state: “confidence intervals are often misinterpreted….the above 95% confidence interval does not imply that the probability that μ falls in the confidence interval is 0.95” (Jaggia & Kelly, 2014, p. 250). So, what do you think this means? [Think about the difference between x-bar and μ.]
Jaggia, S. & Kelly, A. (2014). Essentials of business statistics: Communicating with numbers. McGraw Hill/Irwin: New York, NY.

U.S. Department of Commerce. (2012, April). NIST/SEMATECH e-Handbook of Statistical Methods. Retrieved from http://www.itl.nist.gov/div898/handbook/prc/section1/prc14.htm

* example 1)

The 95% confidence interval can be calculated using the following formula:

X ± Z x σ/√n, where X is the sample mean, Z is the chosen z value from the table provided, σ is the standard deviation, and n is the sample size (“Confidence Intervals”, n.d.). Before looking at a specific example, we can assume that as the Z value increases, the margin of error will also increase, making the confidence interval wider. Z value for 80% confidence interval is 1.28, 95% is 1.96, and 99% is 2.58. The 99% percent confidence interval will be the widest, which makes sense since we must be 99% confident that the interval found will contain the population parameter of interest.

For this example, I will refer back to my previous job as a salesperson. During the financial application to determine credit worthiness, my company ran a credit check on 50 people. The sample mean is 690, with the standard deviation of 30. The 95% confidence interval is (681.6; 698.3). The 99% confidence interval is (679; 700.9). The 80% confidence interval is (685.8; 694.2). For the 80% confidence interval, an upper and lower limit is 8.4 units apart, while the range of 99% interval is about 22 units.

References

Confidence intervals. (n.d.). Math is Fun. https://www.mathsisfun.com/data/confidence-interval.html

OpenStax. (2019). Introductory statistics. Houston, TX: OpenStax College. CC BY-SA. Retrieved from https://cnx.org/contents/MBiUQmmY@23.21:kcV4GRqc@17

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