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$2.$ points$)$ Assume that the DES model in Problem $1$ has been validated. And, the developer has developed a new system model as a new alternative design to replace the existing system design. Now, there are two system designs $($the existing system's design $$ System $1,$ and the alternative$/$new design $$ System $2).$ When these two systems are simulated for $8$ replications, the means for the cycle times in each replication are given in the table below. In each system design, the same random numbers are used for the same events $($random numbers used in two alternative system designs are synchronized $-$ this information is essential in the evaluation and solve the problem using this information$).$

Find out whether the second system is better than the first one $($in terms of the cycle time$-$assume smaller value is better$)$ for the confidence levels $98\%$ and $99\%.$

$\backslash$table$[[$Rep$.$#$,$System $1,$System $2],[1,41,44],[2,48,45],[3,58,51],[4,55,56],[5,55,53],[6,53,51],[7,61,57],[8,57,57]]$