LINK FOR DATASET: https://docs.google.com/spreadsheets/d/1DYbeD7Ww3hU7lC32Lk-zHaby0mxe0-vr/edit?usp=sharing&ouid=109903668686923274818&rtpof=true&sd=true

Overview

We will analyze (fictitious data) about that could have come from Subway restaurants in 4 different cities. Put yourselves in the role of a member of the legal team that is suing Subway. The ultimate goal of the analysis is to inform the actions you take: where to sue and what arguments to make.

Instruction

1. We assume = 12 inches for a subway "footlong" sandwich, with standard deviation =0.25 inches. Use the concepts from previous lessons to answer these questions
   1. What is the probability of observing a subway sandwich of 11 inches or shorter? SHOW YOUR WORK
   2. What size of sandwich would we expect at the 15th percentile?
   3. There is bound to be variability in the manufacturing process. The legal team is willing to accept that Subway cannot change the standard deviation (=0.25 inches) of the manufacturing process. They also agree that the sandwich loaf length is normally distributed. However, the legal team plans to argue that Subway can change the mean length of the sandwich (by adding more dough). The legal team will argue Subway needs to choose such that 99.9% of all baked sandwich loaves are longer than 12 inches. What should be? SHOW YOUR WORK

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 hypothetical 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.

1. Now use the dataset referenced in the Application Activity to calculate the five number summary, sample standard deviation (s) and sample mean () for each city:
2. Paste a graph that contains side-by-side boxplots of the sandwich lengths for each city.
3. Comment on how well Subway is "ensur[ing] consistency"?
4. A hypothesis test against Ho:=12" for each city to see if can reject the Ho.
   1. What should be your alternative hypothesis?
   2. For each city list the test statistic and p-value?
5. Recommend one city in which to file the lawsuit based on your analysis:
   1. What do you think about suing in the other locations, are they also good candidates for a lawsuits?

Ponder / Prove

1. Regarding the city for which you recommended the lawsuit, do you think Subway was deliberate in their shrinking of the sandwich length at that location? Justify your answer.
2. Note that the sample standard deviation was different in each city, and for each city it was different than the population standard deviation =0.25 inches. Is this surprising or concerning? Why or why not?
   1. Based on the data, do you still believe =0.25 inches, which is what we were told to assume?