https://garyrubinstein.wordpress.com/2017/07/28/what-happened-to-the-math-regents-part-ii/

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]]>The dealership will launch the new procedure if 50% or more of the customers will rate it

favorably.

(The dealership cannot see into the future. It is a matter of what the dealership believes will happen based on one sample, not what will actually happen).

Each dot on the graph below represents the proportion of the customers who preferred the new check-in procedure, each of sample size 40, simulated 100 times.

(Each dot represents the proportion of customers in a simulated sample that preferred the new check-in procedure. One hundered simulated samples of fourty customers were generated).

Assume the set of data is approximately normal and the dealership wants to be 95% confident of its results.

(In what do they wish to have 95% confidence? Presumably that at least 50% of customers favor the new procedure, not “its results” as you have already pointed out).

Determine an interval containing the plausible sample values for which the dealership will launch the new procedure.

(The word plausible should be removed. We can identify plausible simulated sample values. But, we can’t identify plausible actual sample values because we don’t know what % of actual customers prefer the new procedure.)

(The decision to move forward or not is based on whether or not it is “plausible” that the one real sample percentage we get came from a population where at least 50% favored the new procedure.)

]]>But nothing to say about “95% confident of our results”, eh?

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