### Question Description

## Final Answer

The P-value of the test statistic? :-/ It isn't really clear to me what the question is asking. It's especially bad that it asks you for a test statistic without telling you what the test is!

1) If there's a test, it's likely to be of the Mayor's belief that >30% of the residents favour annexation. If this is so, we'll get a very high p (>0.5). That's the only test that makes much sense given the wording.

2) But more normally, we would test against a null hypothesis with a fixed value, not an inequality. E.g. we would test the hypothesis that population mean **= 30** (not >30 as in the question).

I'll test 1) since that is the only possible test I can read from the question. But be warned, it doesn't make much sense to me that that is what you'd be asked. It's very badly worded.

Anyway , for a proportion, standard deviation = sqrt(p(1-p))

So sample sd = sqrt(0.33*0.67)

= 0.470

So standard error around the mean = sd/sqrt(n)

= 0.470/sqrt(1000)

= 0.01487

So test statistic t with df=n-1 = 999:

1) For testing pop. mean >30 we have:

t = (0.3-0.33)/0.01487

= -2.018

So P(t, df=999) = 0.978

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