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Politics and Age

APSTAT-PEPGYU

A political pollster was interested in whether there’s any link between age and political preference.

The pollster interviewed $15$ randomly chosen subjects ages $18-24$ and found that $9$ of them said they voted Democrat the last election. This compares to $15$ randomly chosen subjects ages $50$+ where $5$ of them said they voted Democrat last election.

A two-sided test gave a p-value of $0.1432$ and test statistic of $1.46$. The pollster was confused why the sample proportions were so different ($60\%$ vs. $33.33\%$) yet failed to show any significant differences at any common alpha levels ($1\%, 5\%$, or $10\%$).

How might you describe this discrepancy to the pollster?

A

Respondents could have easily lied to the pollster.

B

Conditions were not met in this problem for a two-proportion Z-test.

C

The p-value and test statistic calculations are incorrect for this problem.

D

It is likely a type I error was committed in this test.

E

This test had low power.