Belly Button Ratios 







__________ Height in inches. 






__________ Long Measure  The distance from your belly button to the bottom of your foot in inches. 
__________ Short Measure  The distance from the top of your head to your belly button in inches. 
__________ First Ratio = height/long measure 




__________ Second Ratio = long measure/short measure 




Put your ratios on the board separated by gender. 




Homework: run hypothesis tests to determine if there is a gender difference. 


Note in the small sample size n study below, the differences are not significant. 











Gender 
First 
Second 

Gender 
First 
Second 

Sylvia 
F 
1.66 
1.58 
Ertin 
M 
1.6 
1.66 

Meranda 
F 
1.69 
1.46 
Lee Ling 
M 
1.68 
1.47 

Anastasia 
F 
1.67 
1.49 
Serafin 
M 
1.65 
1.23 

Agnes 
F 
1.61 
1.8 
Kevin 
M 
1.63 
1.58 

Kesarina 
F 
1.67 
1.5 
A1 
M 
1.73 
1.37 

Carolyn 
F 
1.67 
1.44 





Kiumy 
F 
1.63 
1.53 















n 
7 
7 


5 
5 


mean 
1.6540 
1.5431 


1.6572 
1.4624 


stdev 
0.03 
0.12 


0.05 
0.17 




















mean difference 
0.0032 
0.0807 






Ho: µ1µ2=0 



Ho: µ1µ2<>0 


Hyp 
pooled 1/√n 
0.5855 
0.5855 
Test 
degrees freedom 
10 
10 

pooled s 
0.0382 
0.1436 

tstatistic t 
0.1432 
0.9605 

t critical tc 
2.2281 
2.2281 

pvalue 
0.8890 
0.3595 

max c 
0.1110 
0.6405 




Conf 
Error E 
0.0498 
0.1873 
Int 
mean diff – E 
0.0530 
0.1066 

mean diff 
0.0032 
0.0807 

mean diff + E 
0.0466 
0.2681 

Both include zero: Zero cannot be 

ruled out as a possible pop value 




Section 9.4: If n were equal, solve for n. Note that using tc will overestimate n, which is 

considered a "conservative" approach. Better to overestimate than underestimate. 

The desired Error E would be equal to or less than the mean difference. 











n 
1412.27 
31.39 














In theory the first and second ratios approach the Fibonacci Ratio: 


=(1+SQRT(5))/2 








1.6180 






