Question

In recent years there has been considerable discussion about the appropriateness of the body shapes and proportions of the Ken and Barbie dolls. These dolls are very popular, and there is some concern that the dolls may be viewed as having the "ideal body shape," potentially leading young children to risk anorexia in pursuit of that ideal. Researchers investigating the dolls' body shapes scaled Ken and Barbie up to a common height of 170.18 cm (5' 7") and compared them to body measurements of active adults. Common measures of body shape are the chest (bust), waist, and hip circumferences.

Answer 1

These measurements for Ken and Barbie and their reference groups are presented in the table below:

Ken Barbie
Chest Waist Hips Chest Waist Hips
Doll 75.0 56.5 72.0 82.3 40.7 72.7
Human x-bar 91.2 80.9 93.7 90.3 69.8 97.9
Human S 4.8 9.8 6.8 5.5 4.7 5.4

Suppose that the researchers' scaled up dolls suddenly found themselves in the human world of actual men and women.

Convert Barbie’s chest, waist, and hips measurements to z-scores. Do these z-scores provide evidence to justify the claim that the Barbie doll is too thin of a representation of adult women? Justify your response with an appropriate statistical argument.

Answer 2

I have: Chest=(82.3-90.3)/5.5=-1.455
waist=(40.7-69.8)/4.7=-6.191
hips=(72.7-97.9)/5.4=-4.667
This evidence does justify the claim that the Barbie doll is too thin of a representation of adult women.

What I need is the appropriate statistical data to prove my argument. I think I need to determine which is fartherest from 0 by setting the standard deviation to 0 but dont know how to do this.