Where Should YOU Buy Your Next Bagel w/ Cream Cheese and Small Coffee...? By: Kate Engelbert and Mario Canales

The Issue Many prices of different things increase in large cities. Examples of this include the prices of food at restaurants, bottled soda, bottled water, gum etc. We wanted to investigate if the same was true for a bagel and a cup of coffee

New York City

Bucks, Montgomery and Philadelphia Counties

Data Bucks, Montgomery, and Philadelphia Counties X=2.89 S=.5331 N=30 Min=1.95 Q1=2.65 Median=2.90 Q3=3.27 Max=4.11 New York City X=2.62 S=.4715 N=30 Min=1.85 Q1=2.28 Median=2.73 Q3=3.00 Max=3.63

Outlier Test Bucks, Mont, Philadelphia IQR = Q3 – Q1 IQR = 0.62 (IQR X 1.5) = 0.93 Upper Outlier Q = 4.2 Lower Outlier Q1 – 0.93 = 1.72 New York City IQR = Q3 – Q1 IQR = 0.72 (IQR X 1.5) = 1.08 Upper Outlier Q = 4.35 Lower Outlier Q1 – 1.08 = 1.2

NO OUTLIERS!

Two Sample T-Test Assumptions:Check: –2 Independent SRS 2 Independent SRS –2 Normal PopulationsN1=N2=30>30 Or –N1 and N2 >30 ** Our SRS was obtained by going to and using a random number generator to give us 30 random bagel/coffee shops in Bucks, Montgomery, and Philadelphia counties as well as New York City.

Two Sample T-Test Ho: μ PA = μ NY DF = Ha: μ PA < μ NY T = x1 – x2 =  s1 2 /n1 + s2 2 /n2 P (t < ) =.97889

Conclusion We fail to reject Ho because our p-value was greater than alpha, which equals.05. We have sufficient evidence to believe that the mean price of a bagel and a small coffee in Bucks, Montgomery, and Philadelphia counties is equal to the mean price of a bagel and a small coffee in New York City

Confidence Interval (x1-x2) ± t*  s1 2 /n1 + s2 2 /n2= (.00982,.53018) We are 95% confident that the difference between the price of bagels in Bucks, Montgomery, and Philadelphia counties and in New York City falls between.01 and.53 cents.

Price of a Bagel and a Small Coffee Cost (dollars) Bucks, Mont., and Philadelphia New York City

Now Let’s Interpret… From the box and whisker plot, it is obvious that the price of a bagel with cream cheese and a small coffee in our area is actually cheaper than in New York City This is contrary to our prediction that the price would actually be greater in New York City

Bias/Error Some companies listed in the phone book no longer exist Companies may have rounded the price and/or lied

Application This information can be used when deciding where to purchase a bagel and coffee It can also be used (to an extreme) to determine where one chooses to live based on the prices of everyday items

Opinions/ Conclusions After doing this project, it turned out that our predictions were wrong. The price of a bagel and coffee is the same and even a little bit more expensive than that in New York City. This was surprising to us Overall this was a fun project and gave us an opportunity to explore the price of a bagel and coffee. We had a difficult time understanding most of the people on the phone due to the fact that more than half did not speak English. It was quite entertaining