Question

What is the effect of concussions on the brain? Researchers measured the brain sizes (hippocampal volume in microliters) of 25 collegiate football players with a history of clinician-diagnosed concussion and 25 collegiate football players without a history of concussion. Here are the summary statistics:

Group Group Size Mean Standard Deviation

Conclusion 25 5784 609.3

Non-Conclusion 25 6489 815.4

a) Is there evidence of a difference in mean brain size between football players with a history of concussion and those without 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. What effect does this information have on your conclusions in part (a)?

Answer 1

conclusion: sample size(n1) = 25, mean(M1) = 5784, standard deviation(SD1) = 609.3

Non-conclusion: sample size(n2) = 25, mean(M2) = 6489, standard deviation(SD2) = 815.4

a) Ho = there is a no significant difference between mean brain size between football players with a history of concussion and those without concussions

Ha = there is a significant difference between mean brain size between football players with a history of concussion and those without concussions

t-test =

degree of freedom = 25+25-2 = 48

t-stat = -3.463

The P-Value is .000567.

The result is significant at p < .05 at one tail test.

so there is evidence of a difference in mean brain size between football players with a history of concussion and those without concussions at 5 % significance level.

b) mean brain size is increasing between June 2011 and August 2013.