# Hypothesis Testing & Confidence Interval: Alumini Corp

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AluminiCorp is a major producer of aluminum cans that produces 40 billion aluminum cans every year.

You work as a quality control officer for AluminiCorp, and are responsible for ensuring that the aluminum cans produced meet

certain specifications. Each can is supposed to consist of precisely 15 grams of aluminum, and the market price for aluminum is

$0.95 per pound (important note: there are 454 grams in one pound). This file contains data on samples taken from multiple plants

under your purview. Use the data to answer the following questions. Problems 3.1 and 3.2 come from week 7 material, and 3.3

relates to week 8 material. Note that part b (and ONLY part b) of question 3.1 is extra credit. Should you encounter any difficulties

with these problems, the optional problems below are very similar to the questions in this problem set, and the answers to the

optional questions can be found in the back of the textbook. You can also request that the tutor work extensively with you

on the optional problems.

Problem 3.1

Column A contains aluminum content data from a sample of 100 cans taken from your Akron plant. The Akron plant produces 2 billion cans every year.

a) Construct a 95% confidence interval for the population mean aluminum content.

b) EXTRA CREDIT-Construct a 95% confidence interval for the total expenditure on aluminum at the Akron plant. How much money could AluminiCorp save if the Akron plant actually produced cans that were at the target aluminum content?

c) Based on your answer in part (a) (and part (b) if you did that), explain (in plain English) what these results mean.

Problem 3.2

Schlepsi has contracted with AluminiCorp to produce special beverage cans for an upcoming promotion. They want 15% of the Schlepsi cans produced by AluminiCorp to be imprinted with the phrase 'A Winner is You!' along with a promotion code for the winner to submit online to find out what their prize is. You collect a random sample of 750 cans. Of those 750 cans, 156 are stamped with the phrase and promotion code. Construct a 95% confidence interval for the proportion of cans that are stamped with the phrase and a promotion code. Interpret your findings with respect to the 15% target given to you by Schlepsi.

Problem 3.3

Because of the way aluminum cans are stacked when they are shipped, they need to be able to bear a minimum of 200 pounds before collapsing. Column B on the spreadsheet contains the weight at which a sample of 150 cans taken from the Birmingham plant collapsed.

a) Using ? = .05, conduct a one-tailed t test of the hypothesis that average weight bearing capacity is greater than 200 pounds. Use ??200 as your null hypothesis

b) What is the p value associated with your sample mean weight?

c) What conclusions can you draw from these results?

Data set

Akron Birmingham

16.1796178 203.5801455 Important General Information

16.2028448 199.8896338 Desired aluminum content (g/can) 15

16.4455793 197.3928212 Desired weight bearing capacity (lb/can) 200

15.65384454 197.9751835 Price of Aluminum ($/lb) $0.95

15.94133232 198.567427 Grams/Pound 454

15.48619746 199.6945093 Akron Production 2,00,00,00,000

16.09190836 200.2695857

15.30993767 198.4849116 A Winner is You! (Info for 3.2)

15.68198868 196.276912 Sample size 750

15.20009862 199.5660073 Target percentage 0.15

18.09046484 198.4378338 Stamped cans in sample 156

17.43318057 202.5277637

14.60584906 199.7006074

15.65070128 201.6141093

16.8544879 203.5514228

16.12439696 202.0420464

15.00781137 197.8489128

15.23110532 199.4410722

14.9296593 200.8611379

16.14591404 199.4782226

16.22007809 198.6887852

15.02889687 198.1869815

17.01969796 198.9732188

15.66761929 202.5252097

16.66739925 198.3186387

15.54619257 197.5388406

15.10238215 202.0750566

15.78917831 195.7072411

13.80262274 198.8223767

17.39900381 199.0822895

15.5814278 202.2251756

15.46781164 198.0209383

14.67953708 198.1527089

16.36991894 193.537641

16.17831869 201.3686039

15.11675299 198.1079504

14.32516091 196.6625104

16.18107362 199.150221

16.16229003 198.4216164

16.83741285 200.7982339

15.66781364 198.1932872

17.29498976 196.4944739

15.85487383 200.1531272

16.25468684 202.4193954

16.01589137 197.7945179

16.20737701 197.7602805

16.94202142 200.4879465

15.37451558 202.9232188

15.23019548 200.3682942

15.18484609 201.6228821

14.09530965 200.1485907

15.4511616 199.6272285

15.77546954 203.0411499

16.58063784 203.0147053

14.86364103 200.8430809

16.94171121 201.5474164

16.67370146 200.9230809

16.25705581 200.4916391

15.36402133 198.1706507

15.65730963 200.1794502

17.67563044 201.5401965

16.93702797 199.0847799

15.70555281 200.2442445

16.68427837 202.3328602

14.454064 199.9533738

16.42843644 199.8641543

16.87854472 200.9625399

15.78372746 196.9773547

16.1852822 200.6076235

16.68139193 198.373028

16.40417673 197.5494565

14.74201361 196.8037944

16.92496637 202.7411511

17.33390954 200.1020446

15.66368494 201.4307699

16.08972697 204.402705

16.24582961 198.8325566

16.02999706 201.3710427

15.82902709 196.8579907

17.663022 201.0009783

16.88524732 200.9191997

15.25750335 199.8503755

15.10185813 199.8892293

17.58071549 202.4746216

17.33220745 201.7602769

16.94658229 199.2770659

16.8430468 198.206721

16.29516529 199.318184

16.05911755 199.8752744

16.95354285 202.1253917

16.05155805 200.2454852

17.04366098 198.1092912

17.05672851 198.9106576

16.33057601 199.5132331

16.5999534 201.3898726

16.89631516 196.8232323

15.98226264 200.654435

16.83179405 199.1686796

15.72179765 199.474648

15.05402693 200.3260713

199.8027611

199.8659171

198.4431857

200.344783

200.4470659

200.1804884

198.7472918

202.5570048

199.638972

201.4796702

199.947273

201.0269819

199.7485004

199.326607

198.5957323

196.1302763

201.9222083

201.5030365

199.9354555

194.7205982

198.9769015

199.7684813

203.060766

200.0576222

195.0506325

200.5588706

198.1380457

195.1443052

196.8067617

200.3352513

199.5021019

200.7989677

202.0136193

201.8745011

198.6429831

198.7568293

198.6717555

199.318626

201.407014

199.6240068

197.6189164

200.781108

199.0182335

200.5399429

203.2683761

197.1473833

200.5317822

196.3626801

200.5556028

198.1262527

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##### Solution Summary

The solution provides step by step method for the calculation of confidence interval and testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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