By: Bob Luke and Alex

The Myth
• When any given buttered slice of toast slides off a plate, counter, or right off the table, it will disappointingly land butter side down.

The Objective
• Find statistical evidence to suggest that basic laws of physics are in fact incorrect, and as stated by the myth, buttered toast will most likely land butter side down.

The Process
1. Toast 60 pieces of bread
2. Butter 30 randomly selected with one tbsp, other 30 with ½ tbsp
3. In two separate tests, use carefully constructed rig to flip each piece in the exact same way every time and record results

0.6
0.5
0.4
0.3
0.2
0.1
0
1 tbsp
Butter
1/2 tbsp
Butter
The Data
Butter Side Up
Butter Side
Down

The First Test (1)
• 1 Proportion Z Test
Assumptions:
State:
1.
SRS
Check:
2.
n p 10 n

1 p


10
1.
Confirmed
2.
60
60


(.
47 )
(. )


28 2
.


10
10
Ho p down
Ha : p down

.
5

.
5

The First Test (2) z
 p
^  p
( 1
 p p
 
.
5164 P z
 
.
5164

6972 n
We fail to reject Ho in favor of Ha because the p-value
  
. .
probability of the buttered toast falling face down is equal to .5.
p ( 1
 p ) p z

(.
,.
) n
We are 95% confident that the probability of the buttered toast falling face down is between .3404 and .5929.

The Second Test (1)
• 2 Proportion Z Test
Assumptions:
State: Check:
1.
2.
SRS n p n n n
1
2
2

1
 
( p
1
2


10 p p
1 )
10
2
)


10
10
1.
Confirmed
Ho
Ha :
:
2.
p
1

30
30
30



43
57
5



12 9
(.
) .

15 10
10
17 1 10
30

(. )
(. )

15 10 p
2 p
1
 p
2

The Second Test (2) z
 p
1
 p p ( 1
 p )(
2
1
1
 n n
1
2
)
 
.
 
.
) .
1508
We fail to reject Ho in favor of Ha because the p-value
  
. .
probability of the toast buttered with ½ tbsp falling face down is equal to the probability of the toast buttered with
1 tbsp falling face down.
p
1
 p
2
  p

1
1
 p
^
1

 p
2

1
 p
2
 
.
3841 1174
 n
1 n
2
We are 95% confident that the difference between proportions of ½ tbsp and 1 tbsp of butter is between -.3841 and .1174.

The Ultimate Conclusion.
• The laws of physics aren’t kidding, and if your buttered toast falls to the floor, there’s about a 50% chance that it will be ruined. There is also a
50% chance you’ll still get to enjoy your buttered toast if you live by the 5 second rule. Also, spreading more butter won’t worsen your chances of the toast landing butter side down.

The Possible Bias
• Some possible forms of bias that may have affected the results were:
• The butter was never exactly 1 tbsp. Or ½ tbsp.
• 2 different toasters were used
• Environmental conditions because the experiment was done outdoors