Listed in the accompanying table are weights of randomly selected US Army male personnel measured in $1988($from ANSUR I $1988)$ and different weights of randomly selected US Army male personnel in $2012($from ANSURE II $2012).$ Assume that the the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts $($a$)$ and $($b$).$