Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts $($a$)$ and $($b$)$ below. Use a $0\mathrm{.}05$ significance level for both parts.

$\backslash$table$[[,$Male BMI,Female BMI$],[,{}_1,{}_2$