Statistic-QA/5


 

Questions 1-6

A coach is interested in establishing if there is a relationship between his athletes’ squat scores and their 30 m times.  His athletes’ performances are tabulated below:

Athlete Squat 1RM (kg) 30 m time (s)
Ben 140.0 4.0
Paul 140.0 4.2
Chris 162.5 4.3
John 157.5 3.8
Eric 140.0 4.4
Steve 155.0 4.1
Phil 147.5 4.5
Gary 152.5 4.1
James 160.0 3.7
Byron 155.0 4.0

 

The following questions will guide you through the calculation of the correlation coefficient using the method described in the Humongous Book of Statistics Problems (in particular refer to question 14.4).  You should let the athletes’ squat scores be represented by , and their sprint scores by .

  1. Calculate
  2. Calculate
  3. Calculate
  4. Calculate
  5. Calculate
  6. Calculate the correlation coefficient ().Give your answers for questions 1 to 5 correct to 1 decimal place. Give your answer to question 6 correct to 2 decimal places.

Questions 7-11

The same coach believes there is a relationship between his athletes’ power clean scores and their vertical jump performance.  Again, his athletes’ performances are tabulated below:

Athlete Power Clean 1RM (kg) Vertical Jump (cm)
Ben 127.5 73
Paul 85.0 55
Chris 107.5 63
John 135.0 75
Eric 85.0 69
Steve 117.5 70
Phil 75.0 43
Gary 100.0 66
James 80.0 63
Byron 102.5 70

For the following questions refer to questions 14.11 and 14.12 in the Humongous Book of Statistics Problems.  You should let the athletes’ power clean scores be represented by , and their vertical jump scores by .

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  1. Calculate the correlation coefficient ().
  2. Calculate the gradient () of the line of best fit.
  3. Calculate the y-intercept () of the line of best fit.

 

A new athlete (Bill) joins the coach’s group.  Bill can power clean 120 kg and his vertical jump is 65 cm.

  1. Calculate the predicted vertical jump for an athlete who can power clean 120 kg.
  2. True or False. Bill’s vertical jump is better than would be predicted  based on his power clean.

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