The time needed for college students to complete a certain paper-and-pencil maze follows a normal distribution with a mean of 30 seconds and a standard deviation of 2.7 seconds. You wish to see if the mean time is changed by vigorous exercise, so you have a group of 25 college students exercise vigorously for 30 minutes and then complete the maze. It takes them an average of x=30.8 seconds to complete the maze. Use this information to test the hypotheses H0:=30 Ha:30 Conduct a test using a significance level of =0.01

(a) The test statistic

(b) The positive critical value, z* =