Question

What is the effect of concussions on the brain? Researchers measured the brain sizes (hippocampal volume in microliters) of 2525 collegiate football players with a history of clinician‑diagnosed concussions and 2525 collegiate football players without a history of concussions. The table shows the summary statistics.

Group	Group Size	Mean	Standard Deviation
Concussion	25	5784	609.3
Nonconcussion	25	6489	815.4

(a) Is there evidence of a difference in mean brain size between football players with a history of concussions and those without concussions? Let ?? be the mean brain size for players who have had concussions, and let ??? be the mean for those who have not had concussions.

Select the appropriate hypotheses that best describe this research question.

?0:??=??? versus ??:??≠?

?0:??=??? versus ??:??<???

?0:??=???versus ??:??>???

?0:??≠??? versus ??:??>???

Find the standard error, ??, and t-statistic,t, for these data. (Enter your answers rounded to four decimal places.)

SE=

t=

Using either software or Table C, find the degrees of freedom, df. (If you are using software, please enter your answer rounded to two decimal places.)

df=

Determine the P‑value using either software (Option 11) or Table C (Option 22). Select the choice that best represents the P‑value.

P=0.9988 (using Option 11) or 0.95<P<1 (using Option 22).

P‑value cannot be determined using either Option 1 or Option 2.

P=0.0012 (using Option 11) or 0.002<?<0.005 (using Option 22).

P=0.0006 (using Option 11) or 0.001<?<0.002(using Option 22).

Select the appropriate conclusion for the results of the significance test.

a. The sample size is too small to make a conclusion.

b. There is strong evidence that mean brain size is different for football players who have had concussions as opposed to those who have not had concussions.

c. There is weak evidence that mean brain size is different for football players who have had concussions as opposed to those who have not had concussions.

d. There is no evidence that mean brain size is different for football players who have had concussions as opposed to those who have not had concussions.

(b) The researchers in this study stated that participants were "consecutive cases of healthy National Collegiate Athletic Association Football Bowl Subdivision Division I football athletes with (n=25) or without (n=25) a history of clinician‑diagnosed concussion … between June 2011 and August 2013" at a U.S. psychiatric research institute specializing in neuroimaging among collegiate football players.

Select the explanation that appropriately describes how this information could affect a conclusion made regarding the difference between brain sizes of football players with concussion and those without.

a. The fact that these were consecutive cases indicates that they are not a random sample of all of the football players who have or have not had concussions. That could weaken or negate the results of the test. We would need more information about how and why these players were referred to the institute.

b. The fact that these were consecutive cases indicates that they are not a random sample of all of the football players who have or have not had concussions. That could strengthen the results of the test.

c. The fact that these were consecutive cases indicates that they are a random sample of all of the football players who have or have not had concussions. That could strengthen the results of the test.

d. The fact that these were consecutive cases makes no difference to the conclusion made if they were not consecutive cases.

Answer 1

a U.S. psychiatric research institute specializing in neuroimaging among collegiate football players.

Select the explanation that appropriately describes how this information could affect a conclusion made regarding the difference between brain sizes of football players with concussion and those without.

Ans:

c. The fact that these were consecutive cases indicates that they are a random sample of all of the football players who have or have not had concussions. That could strengthen the results of the test.