$\backslash$table$[[$Month$,$Year $1,$Year $2,$Year $3,$Year $4,$Year $5],[$January$,,6381\mathrm{.}07,11016\mathrm{.}55,11965\mathrm{.}68,10580\mathrm{.}74],[$February$,,4405\mathrm{.}83,8264\mathrm{.}14,12761\mathrm{.}98,13420\mathrm{.}87],[$March$,4566\mathrm{.}4,9126\mathrm{.}95,6843\mathrm{.}95,18126\mathrm{.}7,34476\mathrm{.}27],[$April$,6941\mathrm{.}89,10970\mathrm{.}45,20109\mathrm{.}68,19092\mathrm{.}9,19108\mathrm{.}79],[$May$,7047\mathrm{.}23,10189\mathrm{.}28,11148\mathrm{.}64,15384\mathrm{.}01,18109\mathrm{.}54],[$June$,6784\mathrm{.}37,7043\mathrm{.}85,8365\mathrm{.}4,12237,13743\mathrm{.}6],[$July$,5814\mathrm{.}23,6717\mathrm{.}37,9469\mathrm{.}08,13252\mathrm{.}53,18339\mathrm{.}25],[$August$,6906\mathrm{.}38,9139\mathrm{.}72,10221,13819\mathrm{.}77,],[$September$,8075\mathrm{.}13,11315\mathrm{.}19,15161\mathrm{.}41,21755\mathrm{.}64,],[$October$,7913\mathrm{.}56,10838\mathrm{.}4,17731\mathrm{.}08,24838\mathrm{.}1,],[$November$,9054\mathrm{.}18,11150\mathrm{.}94,17508\mathrm{.}99,15955\mathrm{.}6,],[$December$,14114\mathrm{.}58,17592\mathrm{.}2,27566\mathrm{.}89,19370\mathrm{.}7,]]$

Develop a forecast for the sales in August of Year $5$ by using three different forecasting techniques: Three$-$month simple moving average, Weighted moving average with weights $0\mathrm{.}5,0\mathrm{.}3,0\mathrm{.}2($the weight $0\mathrm{.}5$ is given to the most recent observation$),$ and Exponential smoothing method with a smoothing constant of $0\mathrm{.}3.(15$ points$)$

Which forecasting method you considered in Question $1$ is the most accurate according to the Mean Absolute Deviation $($MAD$)$ criterion? Please justify your answer. $(5$ points$)$

Calculate a $95\%$ confidence interval of the forecast made for August of the fifth year. While developing the confidence interval, use the forecasting method identified in question $2$ as the