STAT 250 Midterm: STAT 250 Exam 2 Solutions
STAT 250 Exam 2 Practice Exam 2
PRACTICE EXAM 2
SOLUTIONS
THE DATA
Here we’ll analyze data from a study1comparing mental muscle movements to actual mental
movements. Participants were randomly assigned to perform actual arm pointing move-
ments, or to mentally imagine equivalent arm point motions. The time (in seconds) to com-
plete the motions was recorded. Every participant had the motions timed once pre-fatigue,
and then again after muscle fatigue.
1. Post-Fatigue Comparison
Here we compare actual and mental movements after muscle fatigue. Do mental move-
ments take a shorter amount of time than actual movements for fatigued muscles?
(a) (2 points) State the null and alternative hypotheses.
Solution: µm= average time for mental movement, post-fatigue
µa=average time for actual movement, post-fatigue
H0:µm=µa
Ha:µm< µa
(b) (2 points) Using the randomization distribution below, calculate the p-value: 2/1000 = 0.002
Solution: There are only 2 dots out of 1000 that are less than the observed
difference in means of -1.94, so the p-value is 2/1000 = 0.002.
1Demougeot L. and Papaxanthis C., “Muscle Fatigue Affects Mental Simulation of Action,” The Journal
of Neuroscience, July 20, 2011, 31(29):10712-10720
STAT 250 Exam 2, Page 2 of 6
(c) (2 points) Interpret this p-value in context (note: this is not asking for a conclusion,
but an interpretation of the p-value itself).
Solution: If mental and actual movements took the same amount of time for
fatigued muscles, we would only see a difference as extreme as that observed 2
out of 1000 times.
(d) (2 points) Make a conclusion in context.
Solution: We have enough evidence to conclude that mental movements take
a shorter amount of time, on average, than actual movements when the muscles
are fatigued.
(e) (2 points) How was each dot in the randomization distribution simulated?
Sample with replacement from the original sample
Take a random sample from the population
√Re-randomize the values into groups
Resample with replacement from each group
(f) (2 points) This randomization distribution is best approximated by N( 0,0.697 )
2. Comparing Pre and Post Fatigue
Recall that each person did the movements before and after fatigue. Below are the
summary statistics (pre-fatigue, post-fatigue, and the difference: post-fatigue −pre-
fatigue) for actual and mental movements.
(a) (4 points) How much longer, on average, does it take to do the actual movements
with fatigued muscles as opposed to not fatigued muscles? Calculate a 95% confi-
dence interval. (t∗= 2.364)
Solution:
statistic =xd= 0.875
SE =s
√n=1.146
√8= 0.405
Document Summary
Here we"ll analyze data from a study1 comparing mental muscle movements to actual mental movements. Participants were randomly assigned to perform actual arm pointing move- ments, or to mentally imagine equivalent arm point motions. The time (in seconds) to com- plete the motions was recorded. Every participant had the motions timed once pre-fatigue, and then again after muscle fatigue: post-fatigue comparison. Here we compare actual and mental movements after muscle fatigue. Do mental move- ments take a shorter amount of time than actual movements for fatigued muscles? (a) (2 points) state the null and alternative hypotheses. Solution: m = average time for mental movement, post-fatigue. Ha : m < a (b) (2 points) using the randomization distribution below, calculate the p-value: 2/1000 = 0. 002. Solution: there are only 2 dots out of 1000 that are less than the observed di erence in means of -1. 94, so the p-value is 2/1000 = 0. 002.
