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)
So standard error around the mean = sd/sqrt(n)
So test statistic t with df=n-1 = 999:
1) For testing pop. mean >30 we have:
t = (0.3-0.33)/0.01487
So P(t, df=999) = 0.978
Mar 10th, 2015
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