The following results were obtained from a stratified random sample:

Stratum$1$ : N$1=300$; n$1=50$; $$y$1=10$; s$21$

$=1800$

Stratum$2$ : N$2=50$; n$2=45$; $$y$2=15$; s$22$

$=900$

$($a$)$ Estimate the mean for the whole population.

$($b$)$ Give a $95\%$ confidence interval for the mean.