Hypothesis Testing & Confidence Interval: Alumini Corp

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