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# \$20.00Confidence Interval & Hypothesis Testing: AluminiCorp

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Chapter 1, # 0
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Problem Set 3

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 25% 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, 222 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 25% 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 α = .05, conduct a one-tailed t test of the hypothesis that average weight bearing capacity is greater than 200 pounds. Use μ≥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 15.47627364 199.3191197 Important General Information 16.25300809 196.1894603 Desired aluminum content (g/can) 15 15.11999569 200.819469 Desired weight bearing capacity (lb/can) 200 17.12821758 197.4008484 Price of Aluminum (\$/lb) \$0.95 14.95841164 196.9541354 Grams/Pound 454 16.62262828 198.601525 Akron Production 2,00,00,00,000 17.4344099 199.1030823 16.77039972 200.594914 A Winner is You! (Info for 3.2) 16.93657991 199.8366859 Sample size 750 17.59045086 197.7017951 Target percentage 0.25 16.87607085 198.5101852 Stamped cans in sample 222 15.67249706 200.1761835 16.86511917 199.7111596 17.90573946 203.20863 15.17775543 200.4675432 15.32841109 198.8407948 16.16192098 193.2831003 16.17113741 195.8427919 14.84437602 199.6424708 15.13927603 199.829602 14.19293806 202.2297645 16.87861055 199.5123688 16.78704683 196.9963606 15.93110998 202.8976962 15.97445684 199.4651986 14.82374164 195.8819586 16.65248874 196.2658731 15.85368237 198.9353667 17.1276137 197.3776575 15.41394375 201.2449827 18.14643168 200.3882101 17.44650023 199.4586981 15.91406284 197.258559 16.08657288 201.8327771 14.57528562 199.9237544 15.78569003 201.8797759 16.35993067 197.2741883 16.90455661 198.9060855 17.08001678 201.306428 17.67981027 203.12952 15.00307385 197.5880313 18.02235586 200.770017 18.31396114 199.6042037 16.17412227 200.3562196 14.89863817 197.6999291 19.15029326 201.4098903 14.78680818 200.6468749 15.94135675 197.2351296 16.48966871 200.2705219 16.12965825 202.5289582 17.62024284 199.8539294 15.9577319 197.0641126 16.4466521 196.2411589 17.74705974 199.9160858 15.50526096 200.4799228 15.42229317 199.3440821 17.16445387 196.6145901 16.12035721 197.0078686 15.43168983 200.8555231 14.17811739 197.6860227 13.85487482 202.3703507 15.52091686 201.6222931 15.11069882 199.6895431 16.02259225 197.6535065 15.6528733 197.465094 16.23302485 202.5388245 16.71626315 202.3647369 15.71000072 204.1868007 17.75112971 199.4772066 14.05585019 199.9032613 14.50325164 198.5324121 15.36535808 201.2613546 13.93769835 198.5982248 15.15906593 200.9417309 15.12346623 200.644183 15.90201232 202.3599849 17.03080159 201.4354307 15.77661262 198.2926856 14.73157279 196.7668835 16.3718324 200.2194179 16.02098887 198.5131035 16.50260272 201.4305027 18.73769431 200.5080414 15.6293171 203.2528111 15.56230711 198.2285788 14.60005606 202.0266341 14.70159061 198.0464257 16.05357859 202.2391786 16.09505666 199.8887823 17.01208559 204.6917573 16.96223198 205.5049464 16.92107331 201.5323852 15.8796269 202.1426786 15.04248158 198.6293159 15.62665991 198.4696527 16.81046566 198.0658848 15.46969816 201.5947028 15.01333971 199.6431843 15.7581612 204.0178742 13.90446171 195.5903114 200.7750285 198.8835891 198.5355107 199.0075499 199.3622638 200.8282174 200.8176934 202.0693272 203.6762942 201.2425982 198.1371409 196.3676178 199.7240527 202.2878719 200.6552991 199.5715023 197.5898878 198.1065036 201.3920672 200.0116155 203.9780247 196.4792743 200.5194621 200.8384578 197.17374 199.0221071 198.9069544 200.4825376 200.5840862 198.3625574 199.7129225 197.8628202 196.9725176 197.9689967 197.3090549 199.0256672 203.7578557 201.1244962 199.9638891 198.3316694 201.9706169 198.7732941 198.7301579 201.6086408 200.8218111 197.6294138 198.5320819 203.074328 199.8172824 197.2907057

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Confidence Interval & Hypothesis Testing: AluminiCorp
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