### Question Description

**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.

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## Final Answer

Kindly see attached paper corresponding to the analysis of the Spicy Wings case study. I've also included a plagiarism report in case you need to present it to your University

Running head: SPICY WINGS CASE STUDY

1

SPICY WINGS CASE STUDY

(NAME)

(COURSE)

(DATE)

SPICY WINGS CASE STUDY

2

Introduction

After obtaining his MBA, John Tyler opened a fast food restaurant in a little town. When

analyzing the market, he observed that if he was able of guaranteeing a 30 minutes delivery he

would gain a significant portion of the local market share, since none of the possible competitors

was able of keeping up with such a short delivery time during the busy hours of Saturday

evening. Before embarking on such a project, John has requested a consulting firm to conduct a

hypothesis test to verify if he would be able of satisfying the 30 minutes delivery according to

his current delivery times.

Description of the available data

John Tyler has recorded the time he needs to pick up a new order and drive it in his Spicy

Wings fast food restaurant for 200 orders. These data have then been used to compute the total

delivery time as the sum of the pick-up time and the drive time.

An initial descriptive statistical analysis has been carried out of the total delivery time in

which basic parameters such as the average, standard deviation, minimum, maximum, quartiles

and median have been computed. The data obtained from such analysis is summarized in table 1.

SPICY WINGS CASE STUDY

3

Table 1. Results obtained from the descriptive statistical analysis of the delivery times

Parameter

Average

Standard deviation

Sample size

Minimum

1st quartile

Median

3rd quartile

Maximum

5-number summary

Result (min)

22.52

4.87

200

8.75

19.60

22.90

26.38

31.9

8.75, 19.60, 22.90, 26.38, 31.9

Hypothesis testing

According to the descriptive statistical analysis of the delivery time, it would seem that

John is able of complying with the 30 minutes delivery time in most of the cases. However, in

order to be sure, a hypothesis test has been carried out. The hypotheses being tested are

formulated...

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