A math placement exam is given to incoming college freshmen at Big State University to determine what math course they will start with (PreCalc, Calc 1, Calc 2, etc.). The exam has no time limit – students may work as long as they like before turning in the exam. Students are also allowed to take the exam a second time if they wish. A math professor who administers the exam wonders if the amount of time students use is different among students taking the exam for the first time vs. students taking the exam for the second time (on average). The professor records the following data from two independent random samples. The time was measured in minutes.
Sample 1: students taking exam for the first time
sample size = 41
sample mean = 60.1
sample standard deviation = 5.2
Sample 2: students taking exam the for second time
sample size = 41
sample mean = 62.7
sample standard deviation = 6.3
Does the professor have significant evidence that students taking the exam for the first time use less time than students taking the exam for the second time (on average)? Complete all steps of a hypothesis test (α = .05). Use a computer or calculator to find the exact p-value. What assumptions, if any, are necessary to complete the test?
