Buy it again? A consumer magazine plans to pollcar owners to see if they are happy enough with theirvehicles that they would purchase the same model again.They’ll randomly select 450 owners of American-madecars and 450 owners of Japanese models. Obviously,the actual opinions of the entire population couldn’t beknown, but suppose 76% of owners of American cars and78% of owners of Japanese cars would purchase another.a) What sampling design is the magazine planningto use?b) What difference would you expect their poll to show?c) Of course, sampling error means the poll won’t reflectthe difference perfectly. What’s the standard deviationfor the difference in the proportions? d) Sketch a sampling model for the difference in propor-tions that might appear in a poll like this. e) Could the magazine be misled by the poll, concludingthat owners of American cars are much happier withtheir vehicles than owners of Japanese cars? Explain.

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Author:Amos Gilat
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Buy it again? A consumer magazine plans to poll
car owners to see if they are happy enough with their
vehicles that they would purchase the same model again.
They’ll randomly select 450 owners of American-made
cars and 450 owners of Japanese models. Obviously,
the actual opinions of the entire population couldn’t be
known, but suppose 76% of owners of American cars and
78% of owners of Japanese cars would purchase another.
a) What sampling design is the magazine planning
to use?
b) What difference would you expect their poll to show?
c) Of course, sampling error means the poll won’t reflect
the difference perfectly. What’s the standard deviation
for the difference in the proportions?
d) Sketch a sampling model for the difference in propor-
tions that might appear in a poll like this.
e) Could the magazine be misled by the poll, concluding
that owners of American cars are much happier with
their vehicles than owners of Japanese cars? Explain.
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