While exploring the data and comparing the two previous forecasting methods, you were still not convinced by the forecast accuracy level. Following an in$-$depth analysis, you have decided to check whether there is any seasonal pattern throughout the quarters of the year.

As the manager of this ice cream parlor, you recognize the importance of understanding and leveraging this seasonality to optimize inventory management, staffing levels, and promotional activities. Your goal is to extract and model the seasonality component effectively to make informed business decisions.

Therefore, you redesigned your table as follows:

$\backslash$table$[[$Quarter$,$Ice Cream Sales $($in gallons$),\backslash$table$[[$Average Number$],[$of Ice Cream$],[$Gallons Sold$]],\backslash$table$[[$Expected Number$],[$of Ice Cream$],[$Gallons Sold$]],\backslash$table$[[$Seasonal$],[$Index$]]],[\backslash$table$[[$Year$],[2021]],\backslash$table$[[$Year$],[2022]],\backslash$table$[[$Year$],[2023]]],[$Fall$,400,450,500,450,($h$),0\mathrm{.}53],[$Winter$,300,350,400,350,($h$),0\mathrm{.}41],[$Spring$,1000,1100,1200,1100,($h$),1\mathrm{.}29],[$Summer$,1400,1500,1600,($g$),($h$),($i$)]]$

Complete the table while showing your calculation

$($g$)(2$ points$)($NOTE : round your answer to the nearest integer$)$

$($h$)(2$ points$)($NOTE : round your answer to the nearest integer$)$

$($i$)(2$ points$)($NOTE : round your answer to $2$ decimals$)$

$($j$)(2$ points$)$ We expect total sales for next year $($in $2024)$ to be $4000$ gallons of ice cream. How much can you expect to sell during the fourth quarter of next year $($during Summer $2024)$ accounting for seasonality?

$($k$)(1,$ point$)$ Based on an analysis of the $3$ forecasting techniques, which one would you choose and why?