As a marketing analyst intern, you are asked to assess the di$\backslash$erent digital marketing strategies employed by three e$-$commerce alternatives: StyleHub, TrendSetters, and VogueVilla. Each company employs a distinct strategy. StyleHub relies on influencer collaborations, TrendSetters uses targeted advertisements, and VogueVilla combines email marketing with social media promotion.

To evaluate these strategies, each company provides you with an independent survey of their customers. StyleHub provides you with information on $240$ customers over a $1$ day span, where $160$ of them engaged with the brand at least once by liking, sharing, or commenting on their social medial posts. TrendSetters provides you with information on $65$ customers of which $40$ customers engaged with the brand. Finally, VogueVilla provides you with information on $140$ customers where $85$ of them engaged with the brand.

Unless stated otherwise, assume that the assumptions for all tests are met.e$)[10\mathrm{.}5$marks$]$Usingthedatafromthefirms$,$testwhetherstrategiesthatusesocial media without email marketing provide any improvement over strategies that do use email marketing. Use the p$-$value approach at a $5\%$ significance level. Include all

the steps of hypothesis testing $($hypotheses$,$ decision rule, p$-$value, and conclusion with justification$).$ Show your manual calculations and provide a StatCrunch output confirming your results. $($HINT: You can pool the proportion of the two strategies that do not use email$)($Manual calculations and StatCrunch$)$