SOLUTION: Are attitudes toward shopping changing? Sample surveys show that fewer people enjoy shopping than in the past. A recent survey asked a nationwide random sample of 2577 adults if th

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Question 248992: Are attitudes toward shopping changing? Sample surveys show that fewer people enjoy shopping than in the past. A recent survey asked a nationwide random sample of 2577 adults if they agreed or disagreed that "I like buying new clothes, but shopping is often frustrating and time-consuming." The population that the poll wants to draw conclusions about is all U.S. residents aged 18 and over. Suppose that in fact 62% of all adult U.S. residents would say "Agree" if asked the same questions. What is the probability that 1610 or more of the sample agree?
Answer by stanbon(75887) About Me  (Show Source):
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Are attitudes toward shopping changing?
Sample surveys show that fewer people enjoy shopping than in the past.
A recent survey asked a nationwide random sample of 2577 adults if they agreed or disagreed that "I like buying new clothes, but shopping is often frustrating and time-consuming."
The population that the poll wants to draw conclusions about is all U.S. residents aged 18 and over.
Suppose that in fact 62% of all adult U.S. residents would say "Agree" if asked the same questions.
What is the probability that 1610 or more of the sample agree?
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population mean = sample mean = 0.62
sample std = sqrt[0.62*0.38/2577] = 0.0096
sample proportion = 1610/2577 = 0.6240
z(0.6240) = (0.6240-0.62)/0.0096 = 0.4167
P(x >= 1610) = P(z >= 0.4167) = 0.3385
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Cheers,
Stan H.
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