User Interface Design and Development

You have been retained by Fantastic, Inc., a major e

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commerce company, to offer consultation about a new app that is currently under development. Management believes that Fantastic

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s market share can be increased with the introduction of a new user interface

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$$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

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$$days$,$ separate groups of customers were given the current and new UI design, respectively. I.e

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$$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

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population mean number of unique customer visits for the current UI design

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mu

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population mean number of unique customer visits for the new UI design

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$8$Near the end of your presentation, an executive for Fantastic, Inc. asks you the following

question, "Assuming the same sample of current and new UI design, what would the average

difference in unique customer visits per day have to exceed for you to make the opposite

recommendation?"

Find the answer to her question using the information of the previous $R$ output and the

following equation:

$t=\frac{({\stackrel{}{x}}_1-{\stackrel{}{x}}_2)}{\sqrt[\phantom{2}]{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$

Note: you can assume that the sample variances stay the same, i$.$e$.,$ the denominator does not

change. Select the closest answer, e$.$g$.,$ if you calculate $4\mathrm{.}05$ select $4\mathrm{.}1.$