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# Senator Approval

APSTAT-QKNPNG

Suppose $15$ randomly chosen subjects are questioned on whether they approve of their U.S. senator.

Of these, $3$ ​subjects approved, and $12$ did not approve of their senator. A $90\%$ confidence interval was computed on this data.

Which of the following statements is correct?

A

We are $90\%$ confident that the true proportion of subjects who approve of their senator is between $3\%$ and $37\%$.

B

This survey gives strong evidence that the true proportion of subjects who approve of their senator is less than $35\%$.

C

We are $90\%$ confident that the true proportion of subjects who approve of their senator is between $13.3\%$ and $26.6\%$.

D

We are $90\%$ confident that the true proportion of subjects who approve of their senator is between $17\%$ and $23\%$.

E

A confidence interval in this situation should NOT be done as assumptions are not met.