Mathematics, 26.02.2020 01:25 jonathanmontalv

What is the best dessert to serve at Thanksgiving? One way to decide this is to ask millions of people to make a binary choice: Dessert Option 1 vs. Dessert Option 2 (e. g., apple pie vs. pecan pie). If you randomize what options people must compare, then every dessert will have a "win percentage". This is the percentage of times the dessert beat its (random) opponent when humans were forced to make a binary (!) decision. Luckily, the data journalism website 538 did this very thing!

According to their data, pumpkin pie reigns supreme, winning 81% of head-to-heads with other desserts. You notice that poll was from 2016 and are curious if things are diﬀerent now. So, you conduct a new round of head-to-heads and ﬁnd that in 723 of these, people preferred pumpkin pie. Sadly, you forgot to write down the total number of head-to-heads, n. You do know that your hypothesis test came back statistically signiﬁcant at the α = 0.08 level.

What are all the possible values n could have been?

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