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Suppose we're in the soft drinks industry and we're trying to choose between two new flavors we've produced. We could sample public opinion on the

Suppose we're in the soft drinks industry and we're trying to choose between two new flavors we've produced. We could sample public opinion on the two flavors Passionate Peach and Sinful Strawberry. Let's say we choose to do so by setting up two sampling stalls for each flavor in a busy area and asking 1000 people at each stall if they enjoy the new flavor. 80% of people enjoyed 'Sinful Strawberry' whereas only 75% of people enjoyed 'Passionate Peach'. Marketing team collected some other information while conducting the survey based on the gender of the person sampling the drink. For Passionate Peach flavor, 70% male individuals were asked and for Sinful Strawberry flavor 10% female individuals were asked. The problem is a classic example of the Simpson's Paradox. The paradox states as: A trend or result that is present when data is put into groups that reverses or disappears when the data is combined. Here the group is gender (Male vs Female).

A) If 40% of women liked 'Sinful Strawberry', what percentage of men would like 'Sinful Strawberry'.

B) If 85.7% of men liked 'Passionate Peach', what percentage of women would like 'Passionate Peach'.

C) Justify the Simpson's paradox. [Tips: Show that 80% of people enjoyed 'Sinful Strawberry' and 75% of people enjoyed 'Passionate Peach']

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