Description
The purpose of the assignment is to develop students' abilities in using datasets to apply the concepts of sampling distributions and confidence intervals to make management decisions.
Assignment Steps
Resources: Microsoft Excel®, The Payment Time Case Study, The Payment Time Case Data Set
Review the Payment Time Case Study and Data Set.
Develop a 700-word report including the following calculations and using the information to determine whether the new billing system has reduced the mean bill payment time:
- 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 95% confidence interval and state whether or not the billing system was effective.
- Using the 95% confidence interval, can we be 95% confident that µ ≤ 19.5 days?
- Using the 99% confidence interval, can we be 99% confident that µ ≤ 19.5 days?
- If the population mean payment time is 19.5 days, what is the probability of observing a sample mean payment time of 65 invoices less than or equal to 18.1077 days?
Format your assignment consistent with APA format.
Unformatted Attachment Preview
Purchase answer to see full attachment
Explanation & Answer
Hi! Please see the following file :)
Statistics – Payment Time Reduction
1
In the case given, the population standard deviation is known from historical data and since this is
the case, (population standard deviation is known, 𝜎 = 4.2 days), the z-statistic will be used to
evaluate the claim that the mean payment time is now less than 19.5 days (µ < 19.5 days). Using
the data derived from the 65 samples, the following descriptive statistics parameters were
computed:
n = 65 (number of samples)
mean = 18.10769
standard deviation = 3.96123
From the sample mean, the mean is less than 19.5 days but to generate a conclusion, a confidence
interval is needed in order to have a degree of confidence about the conclusion.
The confidence interval can be computed as follows:
Confidence interval: sample mean ± Zα (𝜎/√𝑛) wh...