Amanda Vonder SchmalzMarlee Levin

About Planet Smoothie!• 3rd Largest American Smoothie Company

• Founded 1995; Atlanta, GA• Bonnie Rhinehardt

– President• Franchise• 16 States– Doylestown, PA

Description of Topic• We went to Planet Smoothie in Doylestown!• Recorded

– Size– Money Spent– Age– Type of Smoothie– Athlete/Non-Athlete– Gender– # Items Purchased

• We wanted to see if there was any association between the variables!

Procedure• Stood where people ordered/paid & recorded

our data• Collected data from every 3rd person to

order• Tests:

– 1-Sample T-Interval – Avg. $ Spent– Test of Independence – Gender v. Smoothie Size– Test of Independence: Athlete v. Smoothie Type– 1-Prop Z-Test: Amount of Regular Sized

Smoothies

1-Sample T-IntervalAmount of $ Spent

1. SRS

2. Normal population or n ≥ 30

3. Population ≥ 10n

Conditions Met T-Distribution 1-Sample T-Interval

1. Systematic Sample – assumed random

2. N=70 ≥ n=30

3. The amount of people that go to Planet Smoothie is greater than 700 people

1-Sample T-Interval: Avg. Amount of $ Spent

• We are 95% confident that the average amount of money spent at Planet Smoothie is between $4.36 and $4.80.

• In repeated samples of 70 subjects, the confidence interval generated would capture the average amount spent 95% of the time.

)7996.4,$35583.4($70

930574.0*96.1)57771.4(/* nstx

Test for Independence: Gender v. Smoothie Size

• We wanted to see if gender had any association with the size of smoothie purchased by Planet Smoothie customers. We removed Medium sized smoothies because not enough customers bought that size to run this test.

First attribute (categorical): Gender

Second attribute (categorical): Size

RowSummary

Column Summary

Gender

M

Gender

F

K

RSize

7 (7.1) 6 (5.9)

28 (27.9) 23 (23.1)

35 29

13

51

64

Test for Independence: Gender v. Smoothie Size

• Categorical Data

• SRS

• All expected cell counts are greater or equal to 5

• All conditions met x2 test distribution x2 test for independence

• Gender and Smoothie Size are categorical variables

• Stratified sample taken assumed random

• All expected cell counts greater than 5!

HO: There is no association between gender and smoothie size.

HA: There is an association between gender and smoothie size.

Test for Independence:Gender v. Smoothie Size

x2 =

00466.0...9.52)^9.56(

71.72)^1.77(

exp2exp)^(

obs

P(df=1|x2>0.00466) = .95 = .05

We fail to reject the HO because the P-value, .95, is greater than the alpha, .05. We have sufficient evidence that gender has no association with smoothie size purchased.

Test for Independence #2: Athletes v. Type of Smoothie

• We also wanted to see if there was an association between customers that were athletes and the type of smoothie they chose. We narrowed it down to cool blended and energy because all of the other types had cell counts of less than 5. Also, this will show us whether or not athletes are conscious of the blast in their smoothie. We predict that the athletes would order energy smoothies more frequently!

First attribute (categorical): Athlete_or_Not

Second attribute (categorical): Type_of_Smoothie

RowSummary

Column Summary

Athlete_or_Not

Y

Athlete_or_Not

N

cool blended

EnergyType_of_Smoothie

18 (16.2) 4 (5.8)

13 (14.8) 7 (5.2)

31 11

22

20

42

Test for Independence #2:Athletes v. Type of Smoothie

• Categorical

• SRS

• All expected cell counts greater than or equal to 5

• Conditions met x2 distribution x2 test of independence

HO: There is no association between athletes/non-athletes and type of smoothie purchase.

HA: There is an association between athletes/non-athletes and type of smoothie purchase.

• Athletes & non-athletes and smoothie type are categorical

• We took a stratified sample assumed random

• All of our expected cell counts are greater than or equal to 5

Test of Independence #2: Athletes v. Type of Smoothie

X2 = 533.1...8.52)^8.54(

2.162)^2.1618(

exp2exp)^(

obs

P(df=1|x2>1.533)=.22 = .05

We fail to reject the HO because the P-value, .22, is greater than the alpha, .05. We have sufficient evidence that there is no association between athletes/non-athletes and their smoothie choice

a

1-Prop Z-Test :Amount of Regular Size Smoothies

State• SRS• n

n(1- ) 10• Pop 10n

Check• Systematic assumed random• (.728)(70)• (.271)(70)

both greater than 10!• Population of amount of

regular smoothies bought is greater than 700!

• Conditions met normal model 1-prop z-test

p̂p̂

5.0:5.0:0

pHpH

A

1-Prop Z-TestMechanics

P(z>3.825) = 6.548 x 10-5

We reject the HO because the P-value, 6.548 x 10-5, is less than the alpha, .05. We have sufficient

evidence that the proportion of regular smoothies sold is greater than .5, or 50%.

835.3)1(

ˆ

nppppz

Gender & Smoothie Choice

• Females – 38/70 = 54.3%– Protein: 0/38 = 0%– Wellness: 12/38 = 31.6%

• Males – 32/70 = 45.7%– Cool blended: 13/32– Wellness: 2/32 = 6.3%

• Cool blended: 22/70 = 31.4%– Favorite smoothie type among

customers• Energy: 20/70 = 28.6%

– Less customers were interested in the energy smoothies as a whole compared to cool blended smoothies

• Kids – 9/70 = 12.9% – There was a very small population of

kids smoothies ordered between males and females. This may have been because there were not a lot of children collected in our sample.

– We conclude that more females came to PS than males. More females are concerned about their weight than males based on the statistics. The energy smoothie was fairly evenly distrubuted among males and females.

Gender

048

12

F

48

12

M

Type_of_Smoothie

cool

ble

nded

Ener

gy

Kids

Prot

ein W

count

Collection 1 Bar Chart

Money Spent• Right Skewed• Unimodal• Median : $4.39• IQR: $0.10• Range: $2.39-$9• Possible outlier at $2.39

• Generally, the customers of PS paid around $4.39. Since the price of a regular happens to be $4.39, we can conclude that the majority of PS customers orders a regular sized smoothie.

10

20

30

40

50

60

70

Money_Spent0 2 4 6 8 10

Collection 1 Histogram

Items Bought v. Gender• Female

– Right skewed– Unimodal– Gap– Median: 1– IQR: 0– Range: 1-4 items

• Male– Right skewed– Unimodal– Median: 1– IQR: 0– Range: 1-4 items

– The males and females have the same median, range, and IQR of number of items bought. From this we can conclude that the amount of items bought is not based upon the gender of the person purchasing the items.

Gender

05

101520253035

F

5101520253035

M

Items_Bought0 1 2 3 4 5 6

Collection 1 Histogram

Athlete v. SizeNon-A: 57/70 = 81.4%Non-A Kids: 12/57 = 21.2%Non-A Reg: 41/57= 71.9%Athletes: 13/70 = 18.6%A Kids – 1/13 = 7.7%A Reg – 10/13 = 76.9%

Overall, more non-athletes got smoothies in general! Regular sizes were more often purchased between the non-a’s and athletes.

From this graph, we can conclude that the customers of PS are more often non-a’s than athletes!

Size

0

10

20

30

40

K

0

10

20

30

40

M

10

20

30

40

R

Athlete_or_NotN Y

count

Collection 1 Bar Chart

Application• If you were to walk into Planet Smoothie…

– Most people in the building would buy a cool blended smoothie

– Most would also order a regular size– An equal amount of males and females would

be in there– There would be more non-athletes than

athletes– You would expect to spend around $4.49 and

purchase one item

Bias & Error• Only went to one PS• Assumed age and athleticism• Only 70 samples; could’ve increased size• Only went on the weekend – rules out anyone

that goes after work, school• Holiday weekend!• Misrecordings• Customers buying for other people (not

present)• Some hours may have been busier than others

Conclusion/Opinions• We had fun!• We thought more athletes would be there• We eliminated blasts as a variable…no one ordered

them as additional items• Not many people ordered more than just a smoothie• Most of our predictions were correct• Less males got wellness and weight loss smoothies• For a better sample, we would change the days we

went, especially since it was a holiday. Also, we would want to go on weekdays as well as weekends to vary our sample.