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Suppose a local group in support of tighter gun restrictions gives a nationwide survey to $200$ randomly chosen subjects.

The question they asked was “Do you favor increased gun control?” In the survey, $66\%$ of respondents said yes, compared to the national average of $64\%$.

How might a statistician explain this difference ($64\%$ vs. $66\%$) to the group?

A

The sample of $200$ subjects was too small to come up with any credible comparisons to the population proportion of $64\%$.

B

Since the sample was conducted by a group that supports tighter gun control, it is probable the poll sampled people who would be more likely to support their cause.

C

Since the sample was conducted by a group that supports tighter gun control, it is likely the question was worded in a confusing or biased manner.

D

Since the group who conducted the survey was local, the respondents might have the opinions of this area, but not necessarily the opinions of the entire country.

E

For samples of size $200$, sampling variability exists where samples can easily be $1\%-3\%$ off the true population proportion.

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