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knowledge of probability and conditional probabilityMTH 410 MODULE 3 ASSIGNMENT

Instructions:

report needs to contain: Introduction that summarizes the problem.

paper formatted in APA that answers the questions posed in the problem by

communicating the results of analysis. Include results of calculations, as well as charts

and graphs, where appropriate.

A conclusion paragraph that addresses findings and what has been determined from the

data and analysis.

No information from other students papers or plagiarism

See example report for formatting Excel file to be completed in addition to report.

The Sky Hospital Consortium consists of 40 hospitals in various parts of the US. After being discharged,

patients are given a survey to determine if they are satisfied with the overall service. In most cases

patients are satisfied. However, some are dissatisfied. In addition, out of those who responded as being

dissatisfied, some filed a formal complaint. In the Excel file, Hospitals, linked at the bottom of the

page, are the results for the patients during a specific year. The Sky Hospital Consortium is divided into

the West, Central, and East Regions.

The Sky Hospital Consortium wants to evaluate the performance of the hospitals. The Consortium wants

to know which hospitals have the fewest complaints. You are to assist in the data analysis by using your

knowledge of probability and conditional probability to help with the ranking of the hospitals, as well as

each Region.

Managerial Report

Prepare a report (see below) with your ranking of the hospitals based on the probabilities and conditional

probabilities, as well as the analysis of each region. Include the following seven (7) items in table format

to support your ranking. Be sure to use five (5) decimal places for your probabilities in the table, as some

of them might be quite small.

1. The probability of a patient responding “Dissatisfied” in each of the three different regions.

2. The probability of a patient filing a formal complaint in each of the three different regions.

3. The probability of a patient filing a formal complaint given a patient response of “Dissatisfied” in

each of the three different regions.

4. The probability of a patient responding “Dissatisfied” for each hospital.

5. The probability of a patient filing a formal complaint for each hospital.

6. The probability of a patient filing a formal complaint given a patient response of “Dissatisfied”

for each hospital.

7. Rank the hospitals within each region for each of the probabilities in 4 – 6. In other words, only

rank the hospitals in the West region against the other hospitals in the West region. Perform the

same analysis for the other two regions. Then, within each region, find the sum of the ranks and

get an overall ranking for each hospital. Evaluate and discuss the meaning of your results. Use

tables, charts, graphs, or visual dashboards to support your findings.

**************

MTH410 Guide to Writing with Statistics

CSU-Global Campus

October, 2014 1 GUIDE TO WRITING WITH STATISTICS 2 Introduction

The purpose of this paper is to provide some general guidance in the writing of papers

using statistics and associated tests. The paper provides some general tips for writing and the use

of statistics. An example prompt is included, followed by a sample paper.

General Tips for Writing a Math Paper: Organization:

o Turn your prompt into headings for paper sections. This will help you to make

sure you include all of the required information and analysis. It also helps the

reader identify the material.

o Your paper needs: A separate title page using APA style requirements (running header, page

numbers, course, instructor, your name, date, etc.). An introduction (often a summary or abstract of the problem). A body of the paper that answers the questions posed in the problem and

includes calculations and graphs associated with this problem. This is

where you can turn your prompt into headings. All references need to be

properly cited. A conclusion paragraph that addresses your findings and what you have

determined from the data and your analysis. A separate sheet for references.

o There are templates that use APA style that you can insert your material into. If

you really struggle with formatting, this may be an option for your first paper or

two. If you use a template, remember to double-check it to remove any extra

instructions or pages or other elements that weren’t used.

In general, numbers less than 10 are to be written in word form. However, if you have

numbers in this range that carry decimals, write them in numeral form.

Never use or interpret a statistic or test that you don’t fully understand.

Target your audience and present as much information as necessary to allow the reader to

make an independent interpretation.

Make use of graphs and tables to display information in an easily understood manner.

Format them the same throughout, and make sure you don’t manipulate axes.

If you are referring to a statistic that is less commonly used, explain how you calculated

it. (It is not necessary to explain mean, but it may be necessary to explain how you set up

an ANOVA test.)

Be clear about your sample and its corresponding population.

Be direct in writing descriptive statistics (The mean in Group A is 22.9 units.).

Translate the meaning of the statistic for the reader. Write plainly and then back it up with

statistical evidence. For example: Men and women scored equally well on this study (t =

0.25, p < 0.01). GUIDE TO WRITING WITH STATISTICS For additional resources see the CSU-Global Guide to Writing and APA Requirements or

visit https://owl.english.purdue.edu/owl/owlprint/672/ 2 GUIDE TO WRITING WITH STATISTICS 3 Prompt for Sample Paper:

Critical Thinking: Heavenly Chocolates

Website transactions are an important segment of sales and distribution today. Heavenly

Chocolates manufactures and sells quality chocolates at its plant and retail store in Bozeman,

MT. Three years ago, the company developed a website and began sales on the internet. Website

sales have exceeded expectations and management is now considering strategies to continue to

increase its sales. To learn more about its sales, Heavenly Chocolates selected a sample of 50

random transactions from its previous month’s sales. The transaction data shows the day of the

week the purchase was made, the type of browser used in the transaction, the time spent on the

website, the number of website pages viewed, and the amount spent by the customer. The data is

shown in a file named Chocolate.

Heavenly Chocolates would like to determine if time spent on the website or the number

of pages viewed influence the total purchase. They would also like to examine any effect that day

of the week and browser type have on sales.

Managerial Report

Prepare a report (see below) using the numerical methods of descriptive statistics presented in

this module to learn how the variables contribute to the sales of chocolate. Be sure to include the

following four (4) items in your report.

1. Descriptive statistics (mean, median, range, and standard deviation) for each of the three

variables along with an explanation of what the descriptive statistics tell us about the

sales.

2. A breakdown using descriptive statistics examining the effect of days of the week on

sales. Evaluate the results.

3. A breakdown using descriptive statistics examining the effect of browser type on sales.

Evaluate the results.

4. Descriptive statistics (correlation coefficient) showing the relationship between sales (in

dollars), and each of the other two variables. Evaluate the relationships between sales (in

dollars) and each of the other variables (time spent and pages visited). Use tables, charts,

graphs, or visual dashboards to support your conclusions. Make recommendations for

continuing to develop sales to the management.

Write a report that adheres to the Written Assignment Requirements under the heading

“Expectations for CSU-Global Written Assignments” found in the CSU-Global Guide to Writing

and APA Requirements. As with all written assignments at CSU-Global, you should have in-text

citations and a reference page.

Your report must contain the following: A title page

An introduction GUIDE TO WRITING WITH STATISTICS 4 A body of the paper that answers the questions posed in the problem and calculations and

graphs associated with this problem.

A conclusion paragraph that addresses your findings and what you have determined from

the data and your analysis. Submit your Excel file in addition to your report.

Note: Prompt adapted from the “Heavenly Chocolate Website Transactions Case Problem 4,” D.

Anderson, D. Sweeney, T. Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for

business and economics. (7th ed.), p. 167,168. The following pages contain the sample paper corresponding to the prompt written

above. Read through it for ideas on how to write your own papers. HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) Heavenly Chocolates Web Sales Analysis

Student Name

MTH410 – Quantitative Business Analysis

Colorado State University–Global Campus

Instructor Name

Date 1 HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 2 Heavenly Chocolates Web Sales Analysis

Website transactions are an important segment of sales and distribution today. Any

business developing a market for online sales would be wise to analyze data from both the

general marketplace and its own specific customer segment. Analysis of this data can provide

insight into further development of sales. Heavenly Chocolates data-mined their transactions for

the previous month to gather a random sample of 50 customer transactions. The sample recorded

the day of the week the purchase was made, the type of browser used in the transaction, the time

spent on their website, the number of website pages viewed, and the amount spent by the

customer. The purpose of this analysis is to determine if the time spent on the website or the

number of pages viewed influences the total purchase. The impact of day of the week and

browser type on sales will also be studied.

Overview of Online Sales

The 50 customers sampled spent a total of $3,406.41 in the previous month. This is an

average of $68.10 per customer. The purchases ranged from a $17.80 to $158.50. The average

customer spent 12.8 minutes on the website. Time spent on the website ranged from 4.3 minutes

to 32.9 minutes. The typical customer viewed almost five pages, with two as the minimum and

ten as the maximum. The data set is summarized below in Table 1.

Table 1

Summary of Online Sales Sample

Time (min) Pages Viewed Amount Spent ($) mean 12.8 4.8 68.1 median 11.4 4.5 62.2 std dev 6.1 2 32.3 min 4.3 2 17.8 HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 3 Table 1

Summary of Online Sales Sample (Continued)

Time (min) Pages Viewed Amount Spent ($) max 32.9 10 158.5 range 28.6 8 140.7 SUM ($) 3406.41 Note: Data compiled from the “Heavenly Chocolate Website Transactions Case Problem 4,” D.

Anderson, D. Sweeney, T. Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for

business and economics. (7th ed.), p. 167,168.

Impact of Day of the Week on Sales

The daily sales breakdown reveals some interesting patterns. Sunday is the lowest sales

day, from the perspective of both total sales ($218.15) and average sales ($43.60). Monday and

Friday were the best days in terms of overall sales performance. Monday had the highest mean

(average) sales at $90.40, while Friday had the highest total sales at $945.43 for roughly 28% of

the sample total. See Table 2 for a complete breakdown of the impact of the day of the week on

amount spent, time spent on the website, and number of pages viewed.

Table 2

Breakdown of Sales by Day of the Week

Sun Mon Tues Wed Thurs Fri Sat Total mean 43.6 90.4 59.3 57 58.8 85.9 54.1 68.1 median 37.2 104.2 67.4 53.4 59.2 70.4 55.6 62.2 std dev 12.8 43.5 14.6 24.5 30.4 33.9 17.7 32.3 min 32.7 26.7 39.1 32.7 17.8 52.1 27.9 17.8 max 64.2 158.5 74.4 94.9 91.6 155.3 78.6 158.5 range 31.4 131.8 35.4 62.2 73.8 103.2 50.7 140.7 count 5 9 7 6 5 11 7 50 Total Sales HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 4 Table 2

Breakdown of Sales by Day of the Week (Continued)

Sun

SUM ($) 218.15 Mon Tues Wed Thurs Fri Sat Total 813.38 414.86 341.82 294.03 945.43 378.74 3,406.41 Time Spent

mean

median 11.4

11.7 15.3

13.3 12.7

10.6 12.4

12 10.9

8.1 12.3

9.7 13.2

13.3 12.8

11.4 std dev 2.2 7.4 6 4.8 7.1 7.8 4.3 6.1 min 8 7.3 7.8 5 6.2 4.3 6 4.3 max 14.3 30.1 24.7 19.5 23.3 32.9 18.1 32.9 range 6.3 22.8 16.9 14.5 17.1 28.6 12.1 28.6 Pages Viewed

mean 4.2 6.4 4 4.2 3.8 4.8 5.3 4.8 median 4 6 4 4.5 4 4 5 4.5 std dev 1.9 2.1 2.1 1.5 2 2.3 1.1 2 min 2 4 2 2 2 3 4 2 max 7 10 7 6 7 10 7 10 range 5 6 5 4 5 7 3 8 Note: Data compiled from the “Heavenly Chocolate Website Transactions Case Problem 4,” D.

Anderson, D. Sweeney, T. Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for

business and economics. (7th ed.), p. 167,168.

By almost every measure, Monday is the best day for sales. Friday follows closely (see

Table 2). It makes logical sense to recommend that the marketing department develop advertising

targeted for Monday and Friday. Weekends are subpar and midweek statistics are nearly

equivalent. Targeting sales or special packages for midweek may produce some increased traffic.

If these recommendations are implemented, follow-up analysis is recommended to see if the

desired results are being produced.

Impact of Browser on Sales HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 5 There were also sales differences revealed by breaking the data down by browser type.

Customers using Internet Explorer to complete their transactions accounted for the highest total

sales at $1,656.81; however, this value was achieved on volume (see Table 3). Internet Explorer

had the lowest average sale at $61.36 while Firefox customers averaged $76.80 per transaction.

Table 3

Breakdown of Sales by Browser

Firefox Internet

Explorer Other Total mean 76.8 61.36 74.5 68.1 median 68 55.6 67.4 62.2 std dev 38.9 29.2 24.6 32.3 min 27.9 17.8 52.2 17.8 max 158.5 126.4 120.3 158.5 range 130.6 108.6 68.1 140.7 count 16 27 7 50 SUM ($) 1,228.21 1,656.81 521.39 3,406.41 Note: Data compiled from the “Heavenly Chocolate Website Transactions Case Problem 4,” D.

Anderson, D. Sweeney, T. Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for

business and economics. (7th ed.), p. 167,168.

The opportunity here is to target premium packages for advertising specific to Firefox.

Value packages could be created for advertising specific to Internet Explorer. This promotion

should be combined with the recommendations given regarding days of the week and subjected

to a follow-up analysis to check for results.

Relationship between Amount Spent and Website Use

The other feature of this analysis is to evaluate the relationship between amount spent by

customers and how much time they spent on the website with the additional variable of number HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 6 of pages viewed also taken into account. For this, a correlation analysis was performed. The

correlation coefficient between time spent on the website and amount spent in dollars was

moderately positive (r = 0.58). A similar moderately positive correlation coefficient (r = 0.60)

was found between the variables of time spent on the website and number of pages visited. The

strongest correlation was found between number of pages viewed on the website and amount

spent. This correlation coefficient (r = 0.72) approaches a strong positive correlation (see Figure

1). This suggests that there may be some merit in trying to guide customers to view more pages.

180.00

160.00

140.00

120.00

100.00 Dollars Spent 80.00

60.00

40.00

20.00

0.00 1 2 3 4 5 6 7 8 9 10 11 Pages Viewed Figure 1. Relationship Between Pages Viewed and Dollars Spent. Data compiled from the

“Heavenly Chocolate Website Transactions Case Problem 4,” D. Anderson, D. Sweeney, T.

Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for business and economics. (7th

ed.), p. 167,168.

A common tactic is to guide customers to pages that have also been viewed by other

customers viewing the product on the current page. Another suggestion is to pair pages and

suggest that customers who purchased the product on the current page also frequently purchased

a product on the linked page. As with previous suggestions, follow-up analysis should be

performed to check results. On a cautionary note, this can be overdone. The statement from HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 7 Essentials of Statistics for Business and Economics that correlation is a measure of linear

association and not causation should also be duly noted (Anderson, et al., 2015).

Conclusion

The analysis of this sample of 50 random customer transactions revealed several items to

be used in the development of continued growth at Heavenly Chocolate. There is positive

correlation between all three variables, but the strongest correlation is between number of pages

viewed and amount of sales. There is adequate reason to pursue linking pages and making

suggestions for customer purchasing. Monday and Friday are the best sales days. Firefox

customers spend the most, but Internet Explorer customers provide the highest volume.

Packaging and marketing strategies can be developed using this information. This analysis

validates the use of statistical tools to provide insight into new strategies. Follow-up analysis is

also mandated to find out if the strategies are producing results. HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample)

References

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., & Cochran, J.J. (2015). Essentials

of statistics for business and economics. (7th ed.). Stamford, CT: Cengage Learning. 8