*label*Mathematics

### Question Description

# The Payment Time Case Study- The Excel has been posted and completed just need paper

**Purpose of Assignment**** **

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.

**Click** the Assignment Files tab to submit your assignment.

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## Tutor Answer

Kindly see attached file with the requested analysis together with the corresponding plagiarism report.I haven't done any editions to the excel worksheet you had uploaded. The rest of calculations needed are shown in the word file. However, if you believe you need to include them as well in the excel let me know to do it

Running head: THE PAYMENT TIME CASE STUDY

THE PAYMENT TIME CASE STUDY

(NAME)

(PROFESSOR’S NAME)

(COURSE)

(DATE)

1

THE PAYMENT TIME CASE STUDY

2

Confidence intervals are a commonly used statistical tool to provide a rapid idea of both

the average value, located in the middle of the interval, and of the variability of the results,

indicated by the limits of the confidence interval (O’Hagan, 2009). Taking this into account, both

the average and the variation of the results need to be calculated when attempting to build a

confidence interval. Another important parameter necessary when establishing the confidence

interval is the desired confidence level. This represents the minimum probability that the

statistician is willing to accept of finding the real population mean within the limits of the

confidence interval (Johnson, 2000).

In this report, different confidence intervals are being used to evaluate if the payment

time of the customers of a hypothetical trucking company is affected by the new company

strategy. In this regard, the managers of the company hope that the new strategy motivates

customers to pay their bills earlier, such that the payment time is decreased to at least 19.5 days.

Evaluation of the descriptive statistics of the payment time case data set

As has been previously indicated, one of the necessary steps to build a confidence

interval for a series of data is to calculate both their mean value and their standard deviation.

Another critical parameter is the sample size being considered, since it is expected that the

broader the sample, the higher the variability of the results within it.

Taking this into account, the first step towards the construction of the necessary

confidence intervals requested to answer the manager’s questions has been the calculation of the

average, standard deviation and sample size of the data provided in the payment time case study

dataset. The obtained results from such analysis are summarized in table 1.

Table 1. Summary of the results obtained from the descriptive analysis of the dataset

THE PAYMENT TIME CASE STUDY

3

Statistic

Value

Average payment time

𝑥̅ =

Sample standard deviation

𝑠=√

Sample size

∑𝑥

= 18.11

𝑛

∑(𝑥 − 𝑥̅ )2

= 3.96

𝑛−1

n = 65 customers

Analysis

In order to build the confidence intervals of the payment time with the gathered data, it

has been assumed that they follow a normal distribution. This assumption is considere...

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