2005 Statistics Olympics

                                                                                                                                 Statistician _________________

                                                                                                                                  Date ______________________

Congratulations on being selected to participate in the 2005 Statistics Olympics.  You will proudly be representing your nation in the Flexibility and Balance Events.  Gold, Silver and Bronze medals will be awarded to the winners of each event.  Prepare to win!

 

A random coin toss prior to the start of the Olympic Games will determine which event you and your teammates will compete in first. The Head Coach of each team will determine the order of competition for each team.  The Trinidad team and Tobago team will compete against each other in two events to settle the question of which country is truly more dominant in Olympic competition.  Additionally, you will be using the data from these events to answer three research questions.

 

Flexibility Competition Rules

Sit with both feet stretched out in front of you.  Reach toward your toes and stretch as far as you can past your toes.   (Yes, you read this correctly)  Record the number of cm that you stretch beyond your toes.  If you reach your toes and are unable to reach beyond your toes, your score is 0.  If you are unable to reach your toes, your score is negative.  You will record two attempts in order.  Additionally, you will be recording the scores of all of your teammates (also, in order.)

 

Your Team

 


Name                 First Score    Second Score                    Name                         First Score   Second Score

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

 

 

The other team

 


Name                 First Score    Second Score                    Name                         First Score   Second Score

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

 

 

 

 

1.      The Olympic Committee does not believe that there is a difference in the first and second attempt at the Flexibility event and wants to eliminate the second attempt.  Using the entire group of the Trinidad team and Tobago team as one SRS, determine if there is a significant improvement (at the 5% level) between the first and second attempt.  State Ho and Ha and use an appropriate t-test to determine the information for the Olympic Committee.   Justify your choice of One Sample, Two Sample or Matched Pairs procedure.   (Reminder:  Not one member of the Olympic Committee has been fortunate enough to have taken Statistics, so explain the results so that they will be understood.)

 

 

 

 

 

 

 

 

 

2.      In the Flexibility event, the best stretch is scored for competition.  Are the results for the Flexibility event significantly different (5% level) for your team and the other team?  Use only the best result from each person.  State Ho and Ha and justify your choice of One Sample, Two Sample or Matched Pairs procedures.  Explain your results so that the journalists covering this event from all over the world can interpret the results for their viewers.

 

 

 

 

 

 

Balancing Event

  With your eyes closed, lift one foot at least two inches off the ground (in front of you).  Do not bend your knee to assist you in this process.  Your hands must rest at your side without touching your legs.  Have your partner time you.  Your balancing time begins when your leg is lifted after your eyes are closed.   Time ends if you either open your eyes or drop your leg to the ground (or fall).  Record your time in seconds.    Record the times of your teammates and the other team in separate areas below.

Your Team

 


Name                               Time in Seconds                          Name                             Time in   Seconds            

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________

 

The other Team

 


Name                               Time in Seconds                          Name                             Time in   Seconds            

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

 

 

3.  The Beijing Police Department has commissioned you to study balancing ability at the Olympic Games to determine the average time an athlete in fine condition (such as YOU) can balance with eyes closed and one leg slightly lifted.  The Police department was told by an “expert” that a healthy, sober person can balance on one leg with eyes closed for 30 seconds. 

 

      A.   Some of the members of the police department believe that 30 seconds just doesn’t sound right.  Use an appropriate t-test to determine whether your team sample differs significantly (at the 5% level) from the belief of the expert.  Justify your choice of t-test.  What recommendation would you make to the police department?  

 

 

 

 

 

      B.  Find the average balancing time of teenage athletes in excellent health.  Then create a 95% confidence interval.  Do the results from this balancing event show that this test is a promising Field Sobriety Test?  Explain.

 

 

 

 

 

 

 

 

 

 

COACHES : Please give me your top three results for each event so I can determine the medal awards.