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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