Question

Third Love is a San Francisco-based bra manufacturer and retailer whose mission is to empower women to feel comfortable and confident in their everyday lives. Third Love is known for taking a very data-driven approach to product development and marketing; this has helped them capture significant market share in the $100 billion bra industry and become one of the fastest growing consumer brands in the US. One e-shopping feature that is hypothesized to improve the user experience and ultimately sell more product is the "See on Other Sizes" feature. When browsing a particular garment, this feature allows the customer to view images of the same garment worn by different sized models. The Product Data Science Team is interested in determining whether increasing the number of "Other Sizes" a customer can view will lead to an increase in the average purchase size (i.e, the average number of items a customer purchases). To investigate this they conduct an experiment with four conditions: . Condition 1: The feature is turned off (i.e., a customer sees the garment worn by just one model). . Condition 2: The feature allows customers to see the garment worn by two different sized models. • Condition 3: The feature allows customers to see the garment worn by three different sized models. Condition 4: The feature allows customers to see the garment worn by four different sized models. (a) (2 points) What is the metric of interest and what is the corresponding response variable? . (b) (2 points) What is the design factor and what are its levels? (c) (1 points) What constitutes an experimental unit in this experiment? (d) (1 point State the null and alternative hypotheses for a test of overall equality in the context of this experiment. Use the notation H; which represents the metric of interest in condition j = 1,2,3,4.

Answer 1

$(a)\ Metric: User\ Experience, \ \ Response\ Var: avg\ purchase\ size. \\ (b)\ Design\ factor: "See\ on\ Other\ Sizes"\ feature. \\ Levels:\ 1. The\ feautre\ is\ turned\ off\ i.e.\ only\ 1\ model\ is\ shown, \\ 2.\ 2\ different\ sized\ models,\ shown. \ 3.\ Three\ different\ sized\ models\\ are\ shown, \ 4.\ Four\ different\ sized\ models\ are\ shown. \\ (c)\ Experimental\ Unit : A\ particular\ customer. \\ (d)\ Null: \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4} \ \ where\ \mu_{i}:mean\ purchase\ size\ of\ a\ customer\\ when\ ith\ design\ factor\ level\ is\ implemented. \\ Alternate: \ \mu_{1}\ne \mu_{2} , \ or\ \mu_{2}\ne\mu_{3}\ or\ \mu_{3}\ne \mu_{4}\ or\ \mu_{4}\ne \mu_{1}\ or\ \mu_{2}\ne \mu_{4} \ or\ \mu_{1}\ne\mu_{3}$