Case Study
Name
Institution
Course
Date
CASE STUDY
Confidence Interval is a category of approximation calculated from the statistics of observed data (Holmes, Illowsky, Dean & OpenStax College, 2017). This is a statistic estimate that assists in giving the statisticians a range of probability or approval for a value that is unknown based on the results derived from a given sample. Additionally, the 95% confidence is normally used in developing the confidence interval. Thus the confidence interval is one of the most recommended statistical tool applicable in ascertaining the sample of a population (Tang, 2016). The 95% interval allows more confidence outcomes when a certain sample was taken is true, it allows a larger interval, that is, researchers can get the point of estimation and the confidence level. As a result, one can be able to ascertain acceptable values when researching different items. Consequently, the 95% confidence interval also gives a range of values that have known probability of the items. As a result, a person may get 95% assurance that the probability is true (Diez, Barr, Çetinkaya-Rundel & Amazon.com, 2016). When a sample is bigger or larger, it is possible to obtain accurate results compared to when a sample is smaller. Smaller samples give a researcher limited results especially when the confidence is being calculated.
Therefore the purpose of this project is utilizing a set of data for the Payment Time Case Study in the application of the models of sample distributions and the Confidence Intervals to come up with effective management conclusions. This report will also describe 95% confidence interval and also ascertain if the billing system was efficient. Apart from the use of 95% confidence interval, the report will prove that 95% is µ ≤ 19.5 days.
Assuming the standard deviation of the payment times for all payments is 4.2 days, construct a 95% confidence interval estimate to determine whether the new billing system was effective. State the interpretation of a 95% confidence interval and state whether or not the billing system was effective
It can be computed as;
Confidence Interval Estimation


SD

4.2

Mean

18.1077

Level of Confidence

95%

Middle Computations


Standard error

0.5209

X value

1.96

Half-width Interval

1.021
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