Background Facts

This information is to provide context for your data analysis and recommendations. Consider your group to be a team of consultants hired by Organix Cereals to analyze the data provided and report your findings formally to the company.

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: 285 grams

Price per box: $5.00

Cost of goods sold (per box): $2.75 (based on target mean weight of 287 grams)

Company Standards: In the automated packaging process, equipment is set to fill boxes with a mean weight of 287 grams and a standard deviation of 4 grams. These are the company standards for the box weights. As a small, independent producer of breakfast cereals, Organix uses older equipment and technology in its packaging process. Accordingly, the process results in boxes that are not always packed with exactly 285 grams (weight stated on label).

The company sets the equipment to a target weight (287 grams) 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. This is a common industry practice.

Company management is concerned if company standards are not met, either through over-filling or under-filling boxes on a large scale.

Government Standards:

Two standards must be met for package weights to be in compliance with government regulations:

1. Penalties can be assessed against a company when any individual package weighs less than the Maximum Allowable Variation (MAV). The Maximum Allowable Variation (MAV) is the limit of "reasonable variation" for an individual package based on the NIST Handbook 133.The MAV is 14.5 grams below the declared box label weight of 285 grams.

2. The company can also be penalized if the average package weight does not at least meet the declared box label weight of 285 grams.

Failure to meet government standards can result in fines of $200,000 or more, litigation, and negative publicity for the company and its brand. The government is only concerned if the company is under-filling boxes.

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 Capstone Project Data.

Analysis: Three templates are provided to guide your analysis. Your group must submit all three completed templates in BlackBoard. The questions in the templates include the minimum requirements for your analysis in this project. Your group may choose to do additional statistical and business analysis beyond the minimum requirements in the templates.

Template 1: Use the data on the tab labeled Cereal Weights n=500.

Template 2: Use data on the tab labeled Cereal Weight n=500 for questions 1 and 2; use data found on the tab labeled Weights after Adjustment n=90 for questions 3-5.

Template 3: Use the data found on the tab labeled Weights and Speeds.

As you perform your calculations, continue to round data to four decimal places.

Hint: Whenever you calculate descriptive statistics using Excel, remember to check not only Summary Statistics but also Confidence Level (defaults to 95% confidence) to save your group some time when required to calculate interval estimates (confidence intervals).

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. Descriptive Statistic Value Analysis/Interpretation

Mean:

Median:

Mode:

Standard Deviation:

Range:

Lowest Value

Highest Value

Proportion of boxes below label weight:

Proportion of boxes above company target weight: Proportion of boxes below MAV:

Skewness:

2. Using Excel, create and insert a frequency distribution and histogram of the box weights. Use 9 or 10 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 symmetric 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 270.5 grams? Does this pose a risk to the company?

5. Based on your analysis, should management have any concerns about the packaging process being out of compliance with the government standards? Explain.

DATA TO USE FOR Q.1/2

248.475

250.071

253.8242

253.825

253.8525

253.85335

253.8809

253.8717

257.1028

257.1136

257.1695

257.1503

257.2468

257.2573

259.18235

259.18315

259.99675

260.00725

262.0053

262.0173

262.018

262.0478

262.0902

262.1025

262.1032

262.28255

266.7518

266.7526

266.7824

266.8008

266.8113

266.8652

266.9907

267.0353

267.0361

267.092

267.0928

268.3961

268.3962

268.3969

268.398

268.42445

268.42525

268.4691

268.48115

268.4845

268.83765

268.866

268.93475

268.93555

268.9919

268.99225

268.9832

269.04815

269.109

269.3033

269.3041

269.33165

269.3218

269.3319

269.33245

269.2726

269.3327

269.4167

269.4175

269.4852

269.51355

269.5422

269.7732

269.80155

269.83575

269.84195

269.84275

269.9388

270.9981

271.061

271.0618

271.2128

271.2695

271.46795

271.52465

271.553

271.82645

271.82725

271.8754

271.8859

271.90375

271.91425

271.9499

272.0367

272.4362

272.4529

272.4991

272.5096

272.547

272.5558

272.5663

272.6037

272.6692

272.6797

272.7259

272.7346

272.7783

272.896

272.9065

272.924

272.93485

272.9527

272.9529

272.9632

272.9573

272.97675

272.981

272.9915

273.03345

273.0659

273.0676

273.0666

273.0771

273.0769

273.0771

273.4063

273.4168

273.463

273.4735

273.6855

273.71815

273.7178

273.72865

273.7266

273.74805

274.315

274.342

274.3525

274.37795

274.37875

274.4247

274.43545

274.4731

274.4836

274.4913

274.49215

274.4941

274.5223

274.5403

274.5405

274.54805

274.54885

274.5508

274.551

274.5686

274.5764

274.5772

274.57915

274.5927

274.7671

274.5776

274.79545

274.806

274.5238

274.8343

274.8521

274.86265

275.1312

275.13135

275.2166

275.2731

275.28725

275.3016

275.4412

275.5424

275.57075

275.64165

275.7042

275.5125

275.73255

275.75505

275.81175

276.1236

276.1279

276.12945

276.138

276.1384

276.15195

276.1661

275.50865

276.2593

276.43545

276.4475

276.4483

276.47585

276.47665

276.59135

276.60105

276.6294

276.6339

276.66225

276.9741

276.0308

277.0548

276.4591

277.0593

277.3143

276.971

273.3711

277.3995

277.432

277.43355

277.4425

277.45145

247.4798

277.50825

277.53485

277.56945

277.5753

274.5932

277.62155

277.6499

277.79165

277.82

277.84835

277.8767

277.90965

278.46245

278.4908

278.495

278.445

258.501

279.15245

279.15705

279.1629

279.20915

279.2196

279.2376

279.26585

279.2942

279.30465

279.3783

279.4075

279.3976

279.408

279.7478

279.8045

279.83285

279.9746

280.00295

280.0313

276.031

280.088

280.12525

280.13575

280.1536

280.1641

280.17305

280.2014

280.22975

280.2581

280.28645

280.2866

280.29105

280.4371

280.4476

280.45655

280.4611

280.4849

280.4851

280.5131

280.5132

280.6073

280.61495

280.61575

280.6178

280.6551

280.67165

280.67245

280.68345

280.7118

280.7119

280.7121

280.7685

280.9717

280.9754

280.9859

281.0237

281.052

281.0802

281.0803

281.08035

281.0805

282.1087

281.13705

281.19375

281.3922

281.4489

281.4492

281.47725

281.5103

281.5623

281.59055

281.619

281.6473

281.6474

281.6475

281.7979

281.8084

281.81745

281.81745

281.8458

281.87415

281.9026

282.1111

283.054

282.168

282.19635

282.2427

282.6216

282.6499

282.6503

282.66785

282.6769

282.6874

282.79015

282.80065

282.82005

282.8484

282.87675

282.9113

282.9121

282.9335

282.9336

282.9399

282.9407

283.0185

283.07365

283.08415

283.10355

283.1319

283.1319

283.16025

283.2065

283.21695

283.3812

283.4721

283.5513

283.5857

283.6034

283.63175

283.6422

283.67055

283.80645

283.86315

283.89735

283.95405

283.9543

283.9824

284.01075

284.0453

284.0461

284.2154

284.2162

284.23755

283.4446

284.27485

284.42565

284.436

284.4363

284.4927

284.493

284.69115

284.81075

284.81155

284.8391

284.8399

284.90585

284.9061

284.9342

284.96255

285.01925

285.6456

285.6775

285.682

285.6925

285.728

285.73425

285.73855

285.74905

285.758

285.7847

285.7863

285.8131

285.8147

285.8597

285.8605

286.0236

286.1532

286.1555

286.20995

286.2383

286.55015

286.60685

286.60685

286.63695

287.24885

287.24965

286.6666

287.3081

287.32615

286.7677

287.33665

287.3457

287.3545

287.3547

287.365

287.3652

287.40065

287.4291

287.4292

287.4569

287.4857

287.4859

287.5607

287.5615

287.57075

287.6275

287.6276

287.6277

287.6558

287.68415

287.75915

287.75995

287.8559

287.91095

287.9393

287.4939

288.1865

288.2148

288.2151

288.235

288.2432

288.2512

288.2513

288.27155

288.2795

288.30785

288.308

288.6782

288.979

288.7803

289.00655

289.00735

289.037

289.06535

289.0656

289.07955

289.0937

288.6093

289.0943

289.12205

289.1504

289.1506

289.2736

289.29215

289.3205

289.34885

289.40555

289.49855

290.0576

290.08595

290.0862

290.14265

290.2941

290.42615

289.626

290.48285

290.5112

290.5776

291.38795

291.38875

292.52405

292.58075

292.63745

294.84875

294.8771

294.91965

295.02855

295.8595

295.86935

295.87

295.8977

295.93575

298.93115

298.9313

298.9595

299.15795

299.1659

299.178

299.25095

299.2512

299.2793

299.5046

DATA TO USE FOR Q. 3/5

278.3011

280.65415

283.2907

282.9505

284.2546

279.6619

283.2907

274.1053

274.61825

285.92725

280.399

291.42715

288.4504

280.4557

293.7274

285.6193

272.6144

288.31255

281.0266

270.90565

286.32805

274.30765

288.93625

282.6709

290.58055

271.5577

285.30745

280.09105

288.4543

277.3978

278.3011

280.65415

283.2907

282.9505

284.2546

279.6619

283.2907

274.1053

270.61825

285.92725

280.399

291.42715

288.4504

280.4557

293.7274

285.6193

273.6144

288.31255

281.0266

270.90565

286.32805

274.30765

288.93625

282.6709

290.58055

271.5577

285.30745

280.09105

288.4543

277.3978

278.3011

280.65415

283.2907

283.9505

284.2546

279.6619

283.2907

274.1053

270.61825

285.92725

280.399

291.42715

288.4504

280.4557

293.7274

285.6193

271.6144

288.31255

281.0266

270.90565

286.32805

274.30765

288.93625

282.6709

290.58055

271.5577

285.30745

280.09105

288.4543

277.3978