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Two brands of coffee were compared. Two independent random samples of 50 people each were asked to taste either Brand A or Brand B coffee, and indicate whether they liked it or not. Eighty four percent of the people who tasted Brand A liked it; the analogous sample proportion for Brand B was ninety percent.

(A) At α = 0.01, is there a significant difference in the proportions of individuals who like the two coffees? Use the p-value approach.

(B) What is the critical value(s) for the test in Part(A)?

So I understand my teacher's solution for part A but I don't really understand how they got the values for B. Can someone explain? I tried looking up tables but I couldn't find where 2.575 came from. I feel like I might be looking at the wrong table or reading them wrong.

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Exact p values cannot always be found in tables. 2.575 comes from being the halfway point between 2.57 and 2.58. Please look at the following table:

https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf

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