Question

A researcher intended to investigate the potential difference in BMI between men and women. He also tried to evaluate the effectiveness of a new physical exercise program in reducing BMI. Table 1 summarized the BMI data. At the beginning of the study (Day 0), 64 men and 49 women were included in the study and their BMI values were measured (defined as BMI_M0 and BMI_F0, respectively). After joining the new physical exercise program for 180 days, the participants’ BMI values were measured again (defined as BMI_M180 and BMI_F180, respectively). Only BMI_M180 data were included in Table 1. BMI_M0 and BMI_M180 were paired by row, i.e BMI_M0 and BMI_M180 values at the same row were from the same male participant.

Calculate 95% CIs of the means in male population and female population, respectively. [i.e. you need to the CIs for men and women separately]

Calculate 95% CI of the difference in the means between men and women. [Don’t forget checking the Equal Variances assumption!] From the CI estimation, is there any significant difference in BMI between men and women?

Now look at the men sample at Day 0 and Day 180. Calculate 95% CI of the difference in means in men between Day 0 and Day 180. From the CI estimation, is the new physical exercise program effective in reducing BMI in men? (i.e. does the new physical exercise program lead to a BMI reduction in men significantly different from Zero ? Attention: this case, the change in BMI between 0 and 180 days of each man should be used for the CI calculation, not directly the values at 0 day and 180 days!)

Table 1. BMI data {BMI_M0 and BMI_M180 were paired by row!!}

BMI_M0	BMI_F0	BMI_M180
29.6	27.1	22.9
19.9	29.8	25.6
21.5	32.8	23.8
15.8	23.5	27.7
22.9	27.8	24.2
28.1	20.1	24
27.5	26.5	22.3
25.3	18	22.9
33.4	12.9	27.5
28.5	24.9	17.6
30.4	31.5	22.5
30.9	16.2	22.4
36.4	29.9	27.6
22.5	20.1	20.7
25.4	18.7	20.7
34	25.6	23.8
31.9	23.8	22.5
28.4	19.4	30.5
30	33.4	18.5
32.4	22.4	20.6
34.7	30.4	25.2
23.7	17.4	20
21	25.8	19.1
35.2	27.2	27
22.9	28.3	24.7
24.3	21.8	24.9
30.1	25.6	27.4
23.5	27.4	26.2
26.1	18.4	24.1
21.3	20.6	30.6
33.6	27.8	23.9
19.4	27.3	24.1
29.5	19.2	26
29.2	17.8	24.3
27.9	33.5	17.3
24.3	23.8	23.4
25.7	18.6	26.4
28.1	22.8	18.9
31	14.7	23.7
25.5	17.7	26
34.1	29.5	25.2
30.6	23.6	25.7
25.6	24	30.1
30.4	27.7	18.4
25.22	25.9	26.1
34.7	32	29.6
29.2	25.4	28.6
21.6	23.8	23.6
24.5	27.3	17.8
28		24.7
19.9		24.2
29.8		23.1
27.6		23
34.2		21.7
22.2		26.6
27.1		20.6
28		22.4
20.2		22.6
22.8		26.6
30.9		26
25.6		29.4
26.8		24.7
26		20.4
31.5		26.8

Answer 1

The CI or the concentration indexes are used to study the changes in the socio-economic inequality between the genders in means of their body mass indexes.The is a standard method to estimate the inequality between the genders in relation to their body mass indexes.The body mass index is a good indicator to minimize and maintain the body fat thus to avoid the health risk from excess body fat.The normal range of BMI is between 18.5-24.9 in males and females.

CI or the concentration index for men is = $\small n - 1\div n=$ 63

$\small 63\div 64=0.98$

95% of CI in men = 0.93

CI index for women is =

$\small 48\div 49=0.97$

95% CI in women is 0.92

The 95% CI difference between the men and women are 0.01

Normally CI is range between 0-1

Calculation of equivalence variance assumption by F-test

ie F=, $\large [$ X=1/n $\tiny \su\sum_{i=1}^{n}Xi$ $\large ]$ and $\large [$ Y=1/n $\tiny \sum_{i=1}^{n}Xi$ $\large ]$ males and females respectively

F=S²X $\small \div$ S²Y

where

*There is a significant difference that is 0.01 between BMI of men and women

*The 95% CI difference of BMI_M0 amd BMI_M180 is 0,ie there is no that much differennce in BMI,that means BMI value is not reached to the normal till 180 days

There is a new introduction of an physical exercise programme is needed to reduce the BMI of males