8.3 Hypothesis Testing

Data Description

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 Job

## you can use this data or your own personal data.
city_sandwich = read.table("http://byuistats.github.io/M330/tstsents/Hathaway_904ed6b35bc65236d04aaa85ffb72c5a.csv",sep=",",header=TRUE)

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.

1. Write out your Null and Alternative hypotheses.
2. What significance level should we use?
3. Examine your collected data.
   A. Make an overall histogram across all three cities. What do you notice about this distribution?
   B. Provide a histogram for each city?. Put the mean of each city in the title of the histogram.
   C. Make a chart with the four box plots on one chart.
   
4. Perform the appropriate statistical hypothesis test and report your results.
   A. By using a rejection rule (RR) approach.
   B. By using the p-value approach.
   
5. After completing your analysis, propose to the lawyers their best plan of action. Should they do a federal lawsuit across all states or take the cases to specific states (that is; which states look like they could be producing sandwiches shorter than 12 inches)
6. Google for the definition of a p-value and find 4 different definitions of p-value from statistics related websites.