Critical value and test statistic

Question

You wish to test the following claim (HaHa) at a significance level of α=0.005

      Ho:p=0.41

      Ha:p<0.41

You obtain a sample of size n=674 in which there are 267 successful observations.

What is the critical value for this test? (Round to three decimal places.) 

Critical value = 

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

Test statistic = 

Answer 1

critical value is from standard normal distribution table (z scores). Since it is a left-tailed test, look at z-score for cumulative probability of 0.005 = -2.575.

sample proportion = phat = 267/674 = 0.396

z-statistic = (0.396 - 0.41)/ sqrt(0.41 * 0.59/674) = -0.739.