Test statistic and p-value

Question

You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly different from 0.72. You use a significance level of α=0.002

      H0:p=0.72

      H1:p≠0.72

You obtain a sample of size n=225 in which there are 150 successes.

What is the test statistic for this sample? (Report answer accurate to three decimal places.) 

test statistic = 

What is the p-value for this sample? (Report answer accurate to four decimal places.) 

p-value = 

Answer 1

sample proportion phat = 150/225 = 0.667

z = (0.667 - 0.72)/sqrt(0.72 * 0.28/225) = -1.771

since this is a 2-sided test p-value = P(z < -1.771) + P(z > 1.771). Since normal distribution is symmetric this is equal to 2 * P(z < 1.771) = 2 * 0.038 = 0.076.