Concussions and their effects have been a hot button issue in sports and for public health as a whole in recent years. Considering just adolescents (ages 0-18), it has been found that there are around 473,000 annual emergency department visits for head trauma, with over 75% of these being diagnosed as some form of mild traumatic brain injury (mTBI). A 2013 article published in the Journal of the American Medical Association by Babcock et al. found that about 29.3% of participants in a three-month follow-up of adolescents with mTBI (n=406) had experienced some form of post-concussion syndrome (PCS), with the most frequently occurring post-concussion symptom being headaches (30.5%).

The long-term effects of concussions has been a primary concern of the state high school athletic association as well. In an attempt to study this, a random sample of student-athletes who had experienced a concussion during this past school year were brought in for a three-month follow up to discuss any potential post-concussion symptoms they had experienced. The attached data includes basic demographic information about the student-athletes, their concussion history and an indicator of whether or not they experienced various post-concussion symptoms as included on the Post-Concussion Symptom Scale (PCSS). Previous history of concussions and presence of a symptom are indicated by 1 in the data set, and a lack of either by 0.

Below are questions that would help provide insight into findings of this research. Please answer each of these and provide interpretations of the results.

1. (15 points) Use descriptive statistics to summarize the proportion experiencing headache (grouped by history of previous concussion and total), the proportion experiencing any symptoms (grouped by history of previous concussion and total) and the mean number of symptoms experienced (grouped by sex and total). Discuss any relevant findings.

2. (25 points) Develop 95% confidence intervals for (a) the proportion of all student-athletes experiencing headaches, and (b) the mean number of symptoms experienced by studentathletes participating in cheerleading. Comment on whether the appropriate assumptions are met for these methods.

3. (25 points) Conduct a hypothesis test at an =0.05 significance level to determine if there is a difference in the mean number of symptoms experienced between male student-athletes and the mean number of symptoms experienced by female student-athletes. Include your hypotheses, test statistic, P-value and conclusion. Comment on whether the appropriate assumptions are met for this test.

4. (25 points) Conduct a hypothesis test at an =0.05 significance level to determine if the proportion of student-athletes experiencing headaches is different than the proportion indicated in the research. Include your hypotheses, test statistic, P-value and conclusion. Comment on whether the appropriate assumptions are met for this test.

5. (10 points) Given your results from the previous questions, what recommendations would you make to the state high school athletic association?