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    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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    https://brainmass.com/statistics/confidence-interval/hypothesis-testing-confidence-interval-alumini-corp-437912

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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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