In the population of typical statistics students, the mean is 75 and the standard deviation is 6.4 on a national exam. For a sample of 25 students, the mean is 72. Use criterion of .05 and the region of rejection in the LOWER TAIL ONLY to decide if this sample represents the population of typical statistics students.

a) Draw the sampling distribution with the critical value(s) clearly identified. Shade the appropriate area.

b) Compute the z-score for the sample mean (show your work).

c) Compare the sample's z-score to the critical value (s) and state your conclusion (two choices: either reject that the sample represents the underlying raw score population or do not reject that the sample represents the underlying raw score population).