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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.
"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.
Hint: make sure you keep your units of measurement consistent (grams v. pounds)!
Excel Tips: The Excel functions =TDIST and =TINV are similar to the functions =NORMSDIST and =NORMSINV and can be used to calculate T critical values. See the Excel helpfile for instructions on the syntax for this function.
General tip for this problem. In part (a), you calculated a confidence interval for aluminum content. The units of your mean and standard deviation are grams per can. For part (b), you need to first convert your sample mean and standard deviation from part (a) from grams per can into dollars per can. "
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