User Interface Design and Development

You have been retained by Fantastic, Inc., a major e$-$commerce company, to offer consultation about a new app that is currently under development. Management believes that Fantastic$$s market share can be increased with the introduction of a new user interface $($UI$).$ The research group at Fantastic has been investigating a new UI design. The new UI design aims to lead to more customer engagement. So far, the alpha and beta tests have been promising.

One of the researchers on your team has voiced concerns about the effects of the new UI design on user engagement. Fantastic would like the UI design to lead to more customer visits on their app per day. The average number of customer visits, measured in number of unique customers using the app per day, for the new UI design can be equal to or higher than the current UI design, but not lower. If the number of customer visits per day is lower for the new UI design, development for the new design would stop.

To compare the customer engagement for the two UI designs, you arranged an experiment in conjunction with the Fantastic research team. On $32$ days, separate groups of customers were given the current and new UI design, respectively. I.e$.,$ there are two groups of customers, one receiving the current UI design, the other receiving the new UI design. For both groups, you measure how many customer visits you get per day.

You offered the idea of testing the customer engagement to isolate any mean differences in the number of customer visits on each UI design. The results of the tests, with customer engagement measured by the number of unique customer visits on the app per day, follow.

Let

$\backslash$mu $1=$population mean number of unique customer visits for the current UI design

$\backslash$mu $2=$population mean number of unique customer visits for the new UI design

For all of the following questions, use a level of significance a $=0\mathrm{.}05.$

Current New

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$278268$You begin your report to the Fantastic, Inc. management team by offering the following

hypothesis pair as a way of representing the problem.

$H_0$:${}_1-{}_{2}0,H_1$:${}_1-{}_2>0$

How would you explain these hypotheses to the management team?

We assume that the current UI design leads to a higher or equal number of unique customer visits

than that of the new UI design. However, if the new UI design leads to a mean number of unique

customer visits that is significantly higher, then we should reject our assumption and continue the

development of the UI design.

We assume that the current UI design and new UI design both lead to the same mean number of

unique customer visits. However, if the average unique customer visits are considerably different, then

we should reject our assumption and stop developing the new UI design.

We assume that the new UI design leads to a higher or equal number of unique customer visits than

that of the current UI design. However, if the current UI design leads to a mean number of unique

customer visits that is significantly higher, then we should reject our assumption and stop

development of the new UI design.

We assume that the new UI design leads to a smaller or equal number of unique customer visits than

that of the current UI design. However, if the current UI design leads to a mean number of unique

customer visits that is significantly lower, then we should reject our assumption and stop the

development of our new UI design.