DD says 58% Americans prefer to drink their coffee. Of the 500 randomly selected, 325 said yes. You are interested in determining if the proportion of Americans who prefer to drink DD coffee is actually more than what is advertised. (a=.05)
I am assuming that a = .05 is given to indicate that confidence interval is 99%.
Based on this: P hat = 325/ 500 = 0.65 and confidence interval = 0.65 + or - 2.576 sq rt ( 0.65 x 0.35/500)
So confidence interval = 0.65 + or - 0.055
=. 0.705 to 0.545
As the population mean 0.58 falls within the confidence interval 0.705 to 0.545, the Americans who prefer to drink coffee is NOT more than what is advertised.
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