A body mass index $($BMI$)$ between $20$ and $25$ indicates a normal weight. In a random survey of $760$ people

from Group A and $701$ people from Group B$,$ it was found that $225$ people from Group A and $240$ people

from Group B were normal weight. Construct a $99\%$ confidence interval of the difference in the proportion

of people from Group A and people from Group B who are normal weight. Then interpret the interval.

Note the subscripts a and $b$ represent people from Group A and people from Group B$,$ respectively.

Therefore sample $1$ is the people from Group A and sample $2$ is the people from Group B$.$