A representative from your company visited a prison and samp

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.

Solution

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.