Test statistic and critical value

Question

You wish to test the following claim (HaHa) at a significance level of α=0.05

      Ho:μ=78.7

      Ha:μ<78.7

You believe the population is normally distributed and you know the standard deviation is σ=12.8. You obtain a sample mean of M=72.6 for a sample of size n=30

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

You will use the z-statistic for this test.

z = (72.6 - 78.7)/(12.8/sqrt(30)) = -2.61

p-value = P(z < -2.61) = 0.0045.