The average length of time for students to register during the enrolment at a certain college has been 70 minutes. A new registration procedure using modern computing machines is being tried. If a random sample of 61 students had an average registration time of 58 minutes with a standard deviation of 15.9 minutes under the new system, test the hypothesis that the mean is now less than 70, using a level of significance of 0.05. Assume the population of times to be normal.

a) Is this a one-tailed or two-tailed test?

b) What test statistic is to be used?

c) What is the decision rule?

d) What is the computed value of the test statistic?

e) What is your decision/conclusion regarding the null hypothesis?