Hypothesis Testing Help

perrywaffles

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Mar 14, 2015
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Hello everyone, I would really appreciate it if I could have my work checked! :)

This is the problem:
A representative from your company visited a prison and sampled 500 prisoners in Oceana, concluding that 90 of them are political prisoners. Test the hypothesis, at the 5% significance level, that one third of the prisoners in Oceana are political prisoners.

Assuming a two-tailed hypothesis test, this is what I did:
H0 = 33.33%
Ha ≠ 33.33%

significance level = 5%
standard error (SE) = sqrt[P(1-P)/n] =
sqrt[0.33(1-0.33)] =
0.021
Degrees of Freedom = n-1 = 500 - 1 = 499
t-score test statistic = (p - P) / SE = 0.18-0.33)/0.021 = -7.30

Then, when trying to find P (t<-7.30), I used an online t-distribution calculator, and got "0.000" as an answer.

Since 0.000 is greater than -7.30, we fail to reject H0.

I still can't shake the feeling that I did something wrong...
Well anyways, many thanks in advance.
 
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