Comparing the Male and Female Body Mass Indexes

Confidence Interval

The purpose of this study is to compare the Body Mass Index of Men and Woman. Body Mass Index is defined asthe ratio:

BMI=

A BMI less than 18.5 is considered underweight and a BMI from 18.5 to 25 is considered normal. BMI readings from 25- 30 are considered overweight and readings above 30 are considered obese.

Two independent simple random samples of the BMI’s of 40 males and 40 females were chosen. (Analysis Tab excel)This sample size is sufficient to insure the normality assumption requirements are met for the confidence interval construction and T Tests discussed later in the report.

Two Statistical techniques were then used to compare the BMI’s of the Men vs. Woman.

Confidence Interval Method (Male –Female BMI Tab)

A 99% confidence interval for the mean BMI of the Male population indicated a value between 24.5286 and 27.4664. A 99% confidence interval for the Female population Mean indicated a value between 23.1002 and 28.3798.

Both these intervals seem to suggest that the population means border the normal to overweight category of the BMI grouping stated above.

Although, based on these confidence interval estimates it is impossible to conclude whetherthe population means male BMI is statistically different than the mean Female BMI since the confidence intervals overlap.

Hypothesis Test(T Test Means tab)

A hypothesis test was performed testing the claim that the mean Male population BMI was greater than the Mean Female population BMI. The conclusion was that the data does not support the claim that Male BMI is greater than Female BMI.

Why should the statistical analysis give such results given the knowledge that men generally weight more than woman? We can support this conclusion by observing that the BMI is a ratio of weight to the square of height. Although men weigh more they are generally taller than woman. Hence the result the Mean BMI of these two groups being approximately the same should come as no surprise.