# Aluminium Content Data

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.

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.

Problem   3.2

Schlepsi has contracted with AluminiCorp to produce special   beverage cans for an upcoming promotion. They want 10% 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,   59 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 10% target given   to you by Schlepsi.

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?

Excel Tips: By default, =TINV assumes a 2-tailed t test. If you want to   calculate a p-value using a 1-tailed t test, simply double the probability   you enter into the formula. =TDIST is not capable of dealing with negative   numbers. If your t test statistic is negative, use =ABS to make it positive   so =TDIST can work correctly.

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