PRACTICE PROBLEMS:

1. Calculate the t-test result for the following unpaired set of data:
   • Group One: 172, 175, 50, 50, 20, 18
   • Group Two: 9.7, 7.0, 10, 15, 2.5, 3.1 Provide the following information: The two-tailed P value, The mean of Group 1 and Group 2, Standard Deviation, and Standard Error of Mean for each group.
2. In a study of absolute errors in active versus passive arm positioning, an investigator collected data (in centimeters) on 20 college-age subjects (from the motor learning laboratory, California State University Northridge, courtesy of Tami Abourezk). Does a significant difference exist in the errors in arm positioning made by the active group (N1 = 10) compared with those made by the passive group (N2 = 10). Calculate the Paired t-test for the two groups.
   • Group One Active Positioning: 2.65, 2.42, 3.30, 0.19, 1.25, 2.0, 3.34, 4.08, 0.70, 2.89
   • Group Two Passive Positioning: 3.30, 2.00, 0.09, 0.04, 4.56, 3.33, 1.02, 0.89, 2.78, 1.65 Provide the following information: The two-tailed P value, The mean of Group 1 and Group 2, Standard Deviation, and Standard Error of Mean for each group. Answer the following question: Does a significant difference exist in the errors in arm positioning made by the Active Group compared with those made by the Passive Group. Support your answer.
3. A biomechanics researcher wanted to test whether good, average, and poor sprinters differed in horizontal foot speed. She classified the sprinters into three groups based on their sprint times. The horizontal foot speed at touchdown in feet per second was then analyzed with the following results (data is fabricated):
   • Poor4, 5, 8, 6, 7, 6
   • Average7, 8, 9, 6, 7, 10
   • Good10, 13, 12, 8, 11, 12 A. What are the mean values for each group? B. What is the standard deviation for each group?
4. A volleyball coach noted that players who practiced jumping during practice time seemed to be able to jump higher in the games. He wondered whether jumping practice increased vertical jump height more effectively than lower extremity weight training. To test this phenomenon, he proposed the null hypothesis, that no significant differences exist between players who practiced jumping, players who participate in lower extremity weight training, and players who do neither exercise. For 6 weeks prior to the start of the season, he randomly divided his team into three groups of 10 players each. Group one (control) practiced regularly without any special jumping or weight training. Group 2 (jumping) spent the last 20 minutes of each practice session in jumping exercises, and group 3 (weight training) spent the last 20 minutes of each practice session doing high-resistance leg presses. Following are the results (in inches) of a vertical jump test taken 2 days before the first game.

• • Control Group: 27, 32, 34, 25, 21
  • Weight Training: 35, 29, 27, 28, 25
  • Jumping: 34, 35, 37, 37, 28 A. What are the mean values for each group? B. What is the standard deviation for each group? C. Do you accept or reject the null hypothesis? Why or why not (provide explanation