A running coach wanted to see whether runners ran faster after eating spaghetti the night before. A group of six runners was randomly chosen for this study. Each ran a 5 kilometer race after having a normal dinner the night before, and then a week later, reran the same race after having a spaghetti dinner the night before. The times for their races are shown in the table below. What test value should be used in a t test for these dependent samples?
A) 5.07
B) 1.07
C) 2.07
D) 2.62

Question

A running coach wanted to see whether runners ran faster after eating spaghetti the night before. A group of six runners was randomly chosen for this study. Each ran a 5 kilometer race after having a normal dinner the night before, and then a week later, reran the same race after having a spaghetti dinner the night before. The times for their races are shown in the table below. What test value should be used in a t test for these dependent samples? 
A) 5.07 
B) 1.07 
C) 2.07 
D) 2.62

Quizplus · Accepted Answer

Because this is a dependent sample t test (because the same group of people is being tested twice), we need to calculate the difference between the two sets of scores (the difference between the normal dinner race times and the spaghetti dinner race times) and then use the t formula to find the t value. With six runners, there are 5 degrees of freedom, so we look up the t value with 5 degrees of freedom and a threshold of 0.05. The closest t value is 2.571, which we round to 2.62, corresponding to answer choice D.

A Running Coach Wanted to See Whether Runners Ran Faster