A statistics professor would like to set the difficulty for an test such that 90% of the 170 students writing complete it in less than 2.5 hours. To estimate the difficulty ahead of delivery, 4 proxies completed the test beforehand with a mean time of 2.2 hours and a standard error of 0.3 hours. A probability table for a normal (z) distribution appears at the end of this test paper.

Question 1

Is there a difference between 90% of students completing the test in under 2.5 hours and being 90% confident that the mean completion time is under 2.5 hours? Explain.

Question 2

If the sample is taken to be representative of the population, would you expect 90% of students to complete the test in under 2.5 hours?