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.