Statistical Analysis for Business Problem Identification in a Cereal Packaging Company

Capstone Project Information

The purpose of this project is to use statistical analysis to identify a possible business problem, verify whether the problem exists, determine whether attempted actions to correct the problem have been effective, and make recommendations for next steps to address the issues.

In this project, you will analyze data for a company that processes and packages breakfast cereal.  Complete the analysis required for each of the three templates and summarize your findings and recommendations in a formal report to management. Justify all responses using your statistics.

Think like a business person as you respond to the questions, particularly those that ask you for analysis, conclusions or recommendations.

The company data on package weights is provided to four decimal places. Please use four decimal places in your calculations.

Complete each of the three templates and the final report before midnight on the dates stated in the course schedule and submit through BlackBoard. You must complete all 4 parts to receive a final grade for the project.

Caution: Here are some common errors students make when working on this project.

1. Defining descriptive statistics instead of analyzing them. Analysis and interpretation mean you must tell management what those numbers are revealing about the packaging process.
2. Not answering all parts of a question or not completing all 4 parts of the project.
3. Ignoring the fact that all numbers given in the project are provided for a reason and are important to your analysis. 
4. Thinking like a student who has to get a project done, rather than thinking like a business manager who has a problem to solve.
5. Not doing any research at all when developing recommendations for the company, or limiting recommendations to just one possible action.
6. Attempting to copy the work of another student or trying to find the answers on the Internet through one of the cheating sites. The project changes in multiple ways every semester. Doing the work is a lot better than being found in violation of the academic honesty policy, which results in a failing grade for the course, not just the assignment.

Capstone Project Information

Background Facts

This information is to provide context for your data analysis and recommendations.

Company: Organix Cereals (a fictional company) is a small producer of specialty organic breakfast cereal. Its signature product is Gluten-Free Organic Crispies, sold directly online to consumers. The company sells approximately 4 million boxes annually.

Box label weight: 567 grams

Price per box: $6.00

Cost of goods sold (per box): $4.00

Company Standards: In the automated packaging process, equipment is set to fill boxes with a mean weight of 574 grams and a standard deviation of 6 grams. This is the company standard for the box weights.  The company sets the weight slightly higher than the weight stated on the box label to avoid penalties imposed by government inspectors if the box weights do not meet the government standards, and to ensure that customers receive the amount of cereal for which they pay.

Government Standards: Penalties can be assessed against a company when any individual package weighs less than the Maximum Allowable Variation (MAV). The MAV is 22 grams below the declared box label weight of 567 grams, which equals 545 grams. The company can also be penalized if the average package weight does not at least meet the declared box label weight of 567 grams. Failure to meet government standards can result in fines, litigation, and negative publicity for the company and its brand.

Capstone Project Part 1 Template

Data: The company recently took a random sample of 500 boxes of their signature cereal and measured their exact weights.  The data that resulted from this sample can be found on the Excel workbook labeled Data Spreadsheets for Capstone Project.

For Template 1, you will use the data on the tab labeled Cereal Weights. This data will also be used for the first part of Template 2. Also for Template 2 you will use data found on the tab labeled Weights after Adjustment. For Template 3 you will use the data found on the tab labeled Humidity.

Capstone Project Part 1 Template

Descriptive Statistics: Using Excel, calculate the following descriptive statistics and then interpret the results in context using a business perspective. The analysis/interpretation should tell management what the descriptive statistic is revealing about the performance of the packaging process.

2. Using Excel, create and insert a frequency distribution and histogram of the box weights. Use the 2^k ≥ n rule to determine how many classes to include in the frequency distribution.
3. Based on the descriptive statistics, the histogram, and the empirical rule, does it appear that the box weights follow a normal distribution with a symmetrical, bell-shaped curve? Justify your response with your data analysis.
4. Assuming the package weights are normally distributed, convert the MAV value to a z-score using the formula z = (MAV – mean)/standard deviation. What is the probability that any individual package weight will fall below the MAV of 545 grams?
5. Based on your analysis, should management have any concerns about the packaging process being out of compliance with the government standards? Explain.
6. Based on your analysis, should management have any concerns about the packaging process from a business perspective? Explain.

Capstone Project Part 2 Template

In the automated packaging process, equipment is set to fill boxes with a mean weight of 574 grams. This is the standard for the population. Population standard deviation is not known.

1. Calculate a 95% confidence interval for the mean weight of the cereal boxes, using the sample data given in the Excel spreadsheet labeled Cereal Weights.
2. Based on the confidence interval for the mean weight of cereal boxes, does this sample of 500 boxes provide evidence that the packaging process is meeting the company standard? Explain.
3. The company engineer decided to make adjustments to the filling equipment to correct the issue. A random sample of 30 boxes was selected and weighed after the adjustment.  The data for this sample can be found in the Excel spreadsheet labeled Weights after Adjustment.  Find the descriptive statistics and the 95% confidence interval for the mean weight of packages after the equipment adjustment. Using the descriptive statistics and the confidence interval, does it appear that the equipment adjustment had any effect on the weight of the packages?  Explain.
4. Using the data from the Weights after Adjustment, conduct a hypothesis test, using this sample data, to determine whether the mean weight of cereal boxes is meeting the company standard mean weight 574 grams after the equipment adjustment, with the level of significance of .05. Consider carefully whether a one-tail test or a two-tail test would be more useful to management.  Use the company standard mean weight as the population mean; population standard deviation is not known.

What conclusions can you draw about the population mean weight based on the hypothesis test?  Was the equipment adjustment enough to meet the company standard?

Capstone Project Part 3 Template

Correlation Analysis

One of the engineers has been reviewing the data and thinks humidity may be a factor that is affecting the packaging process. The engineer tracked the cereal weights for a random sample of cereal packages over 30 days along with the humidity level on that day during production.  The data can be found in the Excel spreadsheet labeled Humidity.

1. Calculate the correlation coefficient,
2. Interpret the correlation coefficient,
3. What next steps would you recommend the company to take based on these results (along with your previous findings)? Be specific, creative, and logical. This question requires you to do some research.

Capstone Part 4: Final Report

Present your analysis and key findings in a formal report to the production manager. The report should be well-organized, state the problem or issue identified through the analysis, state the actions or steps taken to address the issue and the results of those actions, and end with recommended next steps. Do some creative thinking and research to develop your recommendations; include some lower cost solutions along with more expensive solutions.

Statements should be supported by your data analysis—remember, numbers convince! Be selective in your choice of descriptive statistics you include in the report; do not include all of them. Likewise, when reporting the results of a hypothesis test, simply tell the findings, indicate the level of significance, and perhaps include the p-value. Management does not need to see all the calculations in the report.

Report requirements:

Single space within paragraphs; double space between paragraphs; use headings to make it easy for the manager to find information

Professional business writing style: concise, specific, accurate. No fluff. No slang. No grammatical or spelling errors.

Well-supported with data analysis from the templates

No more than 2 pages in length

Use visuals if helpful in supporting your statements