Suppose that 20% of the residents in a certain state suppor an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within 0.04 of the true proportion (i.e., between 0.16 and 0.24)?

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Suppose that 20% of the residents in a certain state suppor
an increase in the property tax. An opinion poll will
randomly sample 400 state residents and will then compute the proportion in the
sample that support a property tax increase.
How likely is the resulting sample proportion to be within 0.04 of the true
proportion (i.e., between 0.16 and 0.24)?
(Hint: Use the sampling distribution of the sample proportion in this case.)
A. O It is certain that the resulting sample proportion will be within 0.04 of
the true proportion.
B. There is roughly a 99.7% chance that the resulting sample proportion
will be within 0.04 of the true proportion.
C. There is roughly a 95% chance that the resulting sample proportion
will be within 0.04 of the true proportion.
D. O There is roughly a 68% chance that the resulting sample proportion
will be within 0.04 of the true proportion.
Transcribed Image Text:Suppose that 20% of the residents in a certain state suppor an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within 0.04 of the true proportion (i.e., between 0.16 and 0.24)? (Hint: Use the sampling distribution of the sample proportion in this case.) A. O It is certain that the resulting sample proportion will be within 0.04 of the true proportion. B. There is roughly a 99.7% chance that the resulting sample proportion will be within 0.04 of the true proportion. C. There is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion. D. O There is roughly a 68% chance that the resulting sample proportion will be within 0.04 of the true proportion.
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