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 A-1 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: µ1-µ2=0


Ho: µ1-µ2<>0

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

pooled s 0.0382 0.1436

t-statistic t -0.1432 0.9605

t critical tc 2.2281 2.2281

p-value 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