Your firm has two key metrics that they will evaluate the product on:

$1.$ The total amount of revenue generated per user session $($mission critical for now$),$

$2.$ A marketing science index that predicts customer satisfaction and the likelihood of return visits $($mission critical for the ongoing sustainability of your firm$).$ Key information on this index:

This index is a validated tool that consists of four questions. These question responses are then scaled to a normative index for each industry. $8\mathrm{.}0$ is a number that indicates a highly successful product at the go$-$to$-$market.

The normative data is held by the market research firm that was hired.

This index is latent in the sense that the overall score an individual is assigned is predictive of how they responded to the four objective measures on the survey.

There is no reason to believe this index lacks validity and reliability as a useful guide in making a selection as to what will stand at market.

Business Goals:

Goal $1$: The company wishes to achieve $60\%$ of customers spending around $$400$ dollars per instance.

Goal $2$: The company wishes to achieve $80\%$ of users being placed above a rating of $8$ on the marketing index

$($note: the marketing index ranges from $1$ through $10$; $1$ is a highly unhappy customer with no chance of returning while $10$ is a highly satisfied customer that has a higher than expected chance of returning and spending more money. $8$ is an industry target$).$

Key Information: Mean $=$ Average; SD $=$ Standard Deviation

Configuration #$1$ Sales: $$425($Mean$),$ $$57\mathrm{.}2($SD$)$

Configuration #$2$ Sales: $$410($Mean$),$ $$48($SD$)$

Configuration #$1$ Marketing Index Metric: $9\mathrm{.}1($Mean$),\mathrm{.}3($SD$)$

Configuration #$2$ Marketing Index Metric: $8\mathrm{.}9($Mean$),\mathrm{.}5($SD$)$

As an analyst, you should immediately notice the following:

Configuration #$1$ sales data has a larger standard deviation than configuration #$2.$ This means there is more variability in the configuration #$1$ sales data. Generally, this implies more risk. The simulation study is designed because analysts want to evaluate how that SD $($a population parameter$)$ might actually move sales revenue up or down if conditions are repeated over numerous trials.

On the other hand, there is larger variability in the configuration #$2$ marketing index data. The SD for configuration #$2$ is $\mathrm{.}5($one half a point on the $10$ point index$).$ So$,$ this could also be problematic because the Index needs to be explained relative to its evaluation goal.

You, as an analyst, are also thinking through how you will explain these results. The last time you presented a report that had SDs in the analysis, some members of your leadership team thought a higher SD was awesome because it meant that revenues were more likely to be higher at the next cycle $($a possibility $--$ but certainly not the point of the SD measurement in statistical methods$).$

Note: the K$-$S test of normality confirmed both of the distributions to be normal. So$,$ we will assume a normal distribution in our simulation of the data sets.

Instructions:

$1.$ Extend the simulation study layout to include the marketing index data. The sales data has already been provided as a completed example of the simulation design.

$2.$ Replicate the simulation study layout to generate a set of plausible values for the sales$/$revenue data. Implement the same design on the marketing index data.

$3.$ Conduct a descriptive analysis of each simulated distribution $($Sales$/$Revenue & Marketing Index$).$

$4.$ Compare the sales revenue data and the marketing index data to the company goals.

$5.$ Conduct an inferential comparison of the distributions of the $($e$.$g$.,$ t$-$test or ANOVA$).$

$6.$ Prepare a $1-$page summary to your chief product officer on which product is most closely matched to the company goals.