What is the value of the test statistic?

Question

In a simple random sample of 270 patients needing surgery, 81 said they obtained a second opinion. Let p be the true proportion of patients needing surgery who seek a second opinion and consider the hypothesis test with H0: p = 0.33 and Ha: p < 0.33. What is the value of the test statistic?

Answer 1

sample proportion = phat = 81/270 = 0.3

population proportion = p0 = 0.33

sample size = n = 270

test statistic = z = (phat - p0)/sqrt(p0*(1-p0)/n) = (0.3 - 0.33)/sqrt(0.3 * 0.7/270) = -1.076.