$($d$)$ Explain why it is necessary to generate two $p-$charts and compare rather than just one $p-$chart for the $37$ days.

Think about this... what if the process on days $1-30($prior to the promotion$)$ was out$-$of$-$control? If it were, would you be able to conclude that an out$-$of$-$control pattern on days $1-37$ was caused by the promotion?

$($e$)$ Explain also why it would be insufficient to compare the chart with days $1-30$ with a chart for days $31-37.$ Remember that you are trying to see the impact of a process change between days $1-30$ and days $31-37.$ Would you be able to see this easily and objectively if you compared the two charts as suggested? Explain why not and you will have answered this question!

$($f$)$ In this particular problem, is the process being out$-$of$-$control undesirable or indicates a problem that needs to be corrected? Explain!

Again, keep in mind the objective is to determine if the promotion had an impact. What would be a "good" impact $($i$.$e$.$ expected effect of the promotion$)$ vs$.$ a "bad" impact here? Now think about the out$-$of$-$control patterns. A "good" out$-$of$-$control pattern is one that indicates a good impact on the process. Is such a