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

1.85 2.37 2.35 2.75 2.95

3.63 2.35 2.75 2.88 3.20

3.15 2.00 1.90 2.05 2.80

3.15 2.00 3.12 2.00 3.08

2.55 2.25 3.11 2.85 2.70

3.00 3.00 2.28 2.33 2.31

Bucks, Montgomery and Philadelphia Counties1.95 1.99 2.90 1.99 3.82

3.38 2.65 2.97 4.11 2.76

2.35 3.27 2.00 2.65 2.86

2.46 2.75 3.28 3.50 2.96

2.65 3.46 3.03 2.84 3.00

3.24 2.56 2.89 2.99 3.51

DataBucks, 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 TestBucks, Mont,

PhiladelphiaIQR = Q3 – Q1IQR = 0.62(IQR X 1.5) = 0.93

Upper OutlierQ3 + 0.93 = 4.2Lower OutlierQ1 – 0.93 = 1.72

New York City

IQR = Q3 – Q1IQR = 0.72(IQR X 1.5) = 1.08

Upper OutlierQ3 + 1.08 = 4.35Lower OutlierQ1 – 1.08 = 1.2

NO OUTLIERS!

Two Sample T-Test

• Assumptions: Check:– 2 Independent SRS 2

Independent SRS– 2 Normal Populations

N1=N2=30>30Or

– N1 and N2 >30** Our SRS was obtained by going to www.yellowpages.com 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:μPA = μNY DF = 57.147Ha:μPA < μNY

T = x1 – x2 = 2.0779

s12/n1 + s22/n2

P (t < 2.0779) = .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* s12/n1 + s22/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

1.85 2.65 4.112.90 3.271.95 2.28 2.73 3.00 3.63

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