Background

Do you want to buy a Footlong and split it with me? How many of us have said that over the years? Well according to a few different people (and lawsuits), we should be saying, “Do you want to get an 11 inch long and split it?”

The figure below captures the outrage that erupted in 2013 over Subway’s shrinking sandwich. OK, maybe the end of the world wasn’t about to happen, but multiple groups sued Subway over the false advertising. Do you think Subway was deliberate in their shrinking of the subway length?

Subway promptly posted this quote to the Chicago Tribune. As the statistical thinkers that you are, what are some words in the statement that give you pause?

“We have redoubled our efforts to ensure consistency and correct length in every sandwich we serve. Our commitment remains steadfast to ensure that every Subway Footlong sandwich is 12 inches at each location worldwide.”1

Below is an image from the New York Post of a picture taken by Mr. Corby who resided in Perth Australia.

Footlong

Your Task

Through a rigorous study across 4 different cities we have collected sandwich lengths at a variety of Subway restaurants in each area. The lawyers that have filed the class action lawsuit2 need you to analyze the data and provide insight with a power point presentation.

Download the data from here.

Please make sure you answer each of the questions below in your slides as these will be used to grade your performance.

Descriptive Data (Slides 1-2):

  1. Title slide with all group member names
  2. Five number summary, sample standard deviation (\(s\)) and sample mean (\(\bar{x}\)) for each city

Challenge the Subway Statement (Slide 3):

We assume the \(\mu\) of 12 inches for a subway sandwich with standard deviation \(\sigma\)=0.25 inches. Use the concepts from the previous lessons to answer these questions on slide 3:

  • What is the probability of observing a subway sandwich of 11 inches or shorter?
  • What size of sandwich would we expect at the 15th percentile?3

What about the Mean (Slide 4-5)?

Subway and the legal system knows that they cannot guarantee that “every” Footlong sandwich is 12 inches. In fact the legal cases would not hold if that was what they were trying to prove. It appears that the Subway focused on “ensure consistency and correct length” instead of “every” in their legal problems4. What we need to prove is that Subway had a consistent (read the average Footlong sandwich) behavior of shorting its customers.

As stated above, our team has properly collected data from four different areas across the US. As the statistical analyst, you need to check each city to see if Subway was ensuring consistency at the correct length. For the data analysis in the study you can use the true mean of 12 inches and true standard deviation of .25 inches.

Download the Subway Excel Sheet and compare each city’s mean Subway Footlong length. For each city calculate the probability of observing the city \(\bar{x}\) or lower (one sided p-value) assuming \(\mu\) and \(\sigma\).

Present your conclusions on Subways “ensur[ing] of consistency” for two of the four cities.

  • Slide 4

    • What is the true standard deviation (\(\sigma\)) of the Subway sandwich lengths in each city?
    • What is your estimate of the standard deviation (\(s\)) for each city?
    • Complete a hypothesis test against \(H_o: \mu = 12"\) to see if your selected city can reject the \(H_o\).
    • Calculate the confidence interval on your \(\bar{x}\) to show your belief about that city’s average sandwich size.

  • Slide 5: Recomend one city to use in the lawsuit.

    • Do you think Subway was deliberate in their shrinking of the subway length at that location?
    • What do you think about the other locations?

  1. http://www.huffingtonpost.com/2013/01/25/subway-footlong-scandal_n_2550156.html↩

  2. ↩

  3. Extra Push: Based on Subway’s statement they need to choose \(\mu\) through the manufacturing process and the average length of a Subway sandwich loaf is normally distributed. They can’t change the standard deviation as it is a fixed part of the manufacturing process. To get more in line with the Subway statement choose \(\mu\) such that 99.9% of all loaves are longer than 12. What should \(\mu\) be?↩

  4. http://blogs.wsj.com/law/2014/04/02/subway-reaches-tentative-deal-with-plaintiffs-over-footlong-claims/↩