A news report states that based on a recent
survey of randomly selected high school seniors,
it is estimated that 30% of all seniors drink
alcohol on a regular basis (margin of error ± 3.5%).a) Identify the
population and the sample.
b) Identify the parameter and the statistic.
c) What reliability (or confidence) do you
associate with this result?
d) Must it be true that between 26.5% and
33.5% of all high school seniors
drink alcohol on a regular basis?
e) A friend asks you what this result means.
Explain…without resorting to any symbols or
formulas.
A public interest group is interested in
people’s opinions about gun control. Random
samples of voting age citizens are drawn in each
of 3 states: Texas, Montana and New York. Each
person is asked "Do you favor tougher gun
control legislation?"a) In Texas, 1000
people are sampled; 402 answer YES. Give an
estimate and margin of error for the percentage
of all Texans who favor gun control legislation.
b) In Wyoming another 1000 people are sampled;
378 answer YES. Give an estimate and margin of
error for the percentage of all Montanans who
favor gun control legislation.
c) In New York 2000 people are sampled; 965
answer YES. Give an estimate and margin of error
for the percentage of all New Yorkers who favor
gun control legislation.
d) What reliability is associated with each of
your results?
e) What are the approximate populations of
Texas and Wyoming? (The answer can be found in
the library or somewhere on the internet.)
f) Compare the results from a, b and d. Does
the margin of error depend on the size of the
(state) population that is sampled from?
g) The correct margin of error for the result
in Texas is approximately ±
3.2%. A friend suggests that, since twice as many
people are surveyed in New York, the margin of
error ought to be twice as small…that is,
the New York margin of error should be ± 1.6%. Is your friend
right?