3. BMI is often used as a proxy for overall health and body composition; a perso
ID: 3354895 • Letter: 3
Question
3. BMI is often used as a proxy for overall health and body composition; a person with a BMI 30 or greater is defined as obese, a person with a BMI 25.0 to 29.9 is defined as overweight, and a person with a BMI under 25.0 is neither. A researcher is interested in seeing if there is an association between gender and body composition (as measured by BMI) in U.S. adults 20 and older. He selects a random sample of 210 U.S. adults 20 and older. The data are summarized in the table below.
Obese
Overweight
Neither
Total
Male
35
38
23
96
Female
47
43
24
114
Total
82
81
47
210
a. What type of variable is gender? What type of variable is body composition?
b. Make an appropriate display for the distribution of
i. body composition for the individuals in this sample.
ii. body composition for females in this sample.
iii. body composition for males in this sample.
c. What percent of females in this sample are neither overweight nor obese?
d. What percent of males in this sample are neither overweight nor obese?
e. What percent of individuals in this sample are neither overweight nor obese?
f. Do you expect the percent of males in the population who are neither overweight nor obese to be exactly the same as your answer to part f? Why or why not?
Obese
Overweight
Neither
Total
Male
35
38
23
96
Female
47
43
24
114
Total
82
81
47
210
Explanation / Answer
Ans:
a)gender and type of body composition are categorical variables.
b)
Prob. distribution of body composition of individuals=[0.390 0.386 0.224]
P(male)=0.457
P(female)=0.543
c)As,P(female and neither)=0.114,so 11.4% of females are neither obese nor overweight.
d)As,P(male and neither)=0.1104,so 11% of males are neither obese nor overweight.
e)P(neither)=0.110+0.114=0.224
So,percent of individual neither obese nor overweight is 22.4%
Obese Overweight neither Total Male 35 38 23 96 Female 47 43 24 114 Total 82 81 47 210 Joint probability distribution Obese Overweight neither Total Male 0.167 0.181 0.110 0.457 Female 0.224 0.205 0.114 0.543 Total 0.390 0.386 0.224 1.000Related Questions
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