SWIMMER’S FLEXIBILITY STUDY Swimming requires complete body movement as defined in sports science. A swimmer’s flexibility helps in his/her movement in water, thus making him/her a faster swimmer. In a study conducted to determine if there is an improvement in swim speed after doing flexibility exercise, 15 swimmers of the same characteristics were randomly selected. They were asked to do a 25-m freestyle and their swim speed (in seconds) were recorded. After this, a flexibility exercise was done. All the swimmers were then asked to do another 25-m freestyle and their swim speed (in seconds) were also recorded. The data collected are given below and can also be found in the worksheet “swim_speed”of excel file “exer3_data.xlsx”. R outputs can be found in the file “exer3_outputs.pdf”. (Use before – after in your computations Swimmer 1 2 3 4 5 6 7 8 Before 16.87 19.42 20.04 22.82 24.24 17.76 23.91 17.17 After 15.82 18.47 20.43 21.76 23.88 18.12 20.96 16.03 Swimmer 9 10 11 12 13 14 15 Before 17.45 15.53 22.15 18.26 16.65 20.51 18.46 After 18.48 15.41 20.91 19.18 14.45 18.86 19.89 1. a.The samples above are ____________ (related/independent) samples. b. At 5% alpha, perform test(s) to determine which test procedure should be used to compare the two populations involved. For EACH test, indicate the following: Ho (in words): Ha (in words): Test Procedure: p-value: Conclusion: 2. Based on the results in #1b, the appropriate test procedure to answer the objective of the researchers is a ____________ (parametric/non-parametric) test procedure. d.A point estimate of the average difference in swim speed of swimmers before and after doing flexibility exercise is __________. e. At 5% level of significance, test if the there is an improvement in swim speed of the swimmers after doing flexibility exercise. Ho: (in symbols) _________; (in words) The average swim speed of swimmers before doing flexibility exercise is ____________ the average swim speed of swimmers after doing flexibility exercise. Ha: (in symbols) _________; (in words) The average swim speed of swimmers before doing flexibility exercise is ____________ the average swim speed of swimmers after doing flexibility exercise. Test Procedure: _________________ Justify your choice of test procedure: p-value: ______________ Conclusion: At alpha = 0.05, _________________________________________ ________________________________________________________________ ________________________________________________________________
SWIMMER’S FLEXIBILITY STUDY
Swimming requires complete body movement as defined in sports science. A swimmer’s flexibility helps in his/her movement in water, thus making him/her a faster swimmer. In a study conducted to determine if there is an improvement in swim speed after doing flexibility exercise, 15 swimmers of the same characteristics were randomly selected. They were asked to do a 25-m freestyle and their swim speed (in seconds) were recorded. After this, a flexibility exercise was done. All the swimmers were then asked to do another 25-m freestyle and their swim speed (in seconds) were also recorded. The data collected are given below and can also be found in the worksheet “swim_speed”of excel file “exer3_data.xlsx”. R outputs can be found in the file “exer3_outputs.pdf”.
(Use before – after in your computations
| Swimmer | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Before | 16.87 | 19.42 | 20.04 | 22.82 | 24.24 | 17.76 | 23.91 | 17.17 |
| After | 15.82 | 18.47 | 20.43 | 21.76 | 23.88 | 18.12 | 20.96 | 16.03 |
| Swimmer | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| Before | 17.45 | 15.53 | 22.15 | 18.26 | 16.65 | 20.51 | 18.46 |
| After | 18.48 | 15.41 | 20.91 | 19.18 | 14.45 | 18.86 | 19.89 |
1. a.The samples above are ____________ (related/independent) samples.
b. At 5% alpha, perform test(s) to determine which test procedure should be used
to compare the two populations involved. For EACH test, indicate the following:
Ho (in words):
Ha (in words):
Test Procedure:
p-value:
Conclusion:
2. Based on the results in #1b, the appropriate test procedure to answer the
objective of the researchers is a ____________ (parametric/non-parametric)
test procedure.
d.A point estimate of the average difference in swim speed of swimmers before
and after doing flexibility exercise is __________.
e. At 5% level of significance, test if the there is an improvement in swim speed
of the swimmers after doing flexibility exercise.
Ho: (in symbols) _________; (in words) The average swim speed of swimmers
before doing flexibility exercise is ____________ the average swim speed of
swimmers after doing flexibility exercise.
Ha: (in symbols) _________; (in words) The average swim speed of swimmers before doing flexibility exercise is ____________ the average swim speed of
swimmers after doing flexibility exercise.
Test Procedure: _________________
Justify your choice of test procedure:
p-value: ______________
Conclusion: At alpha = 0.05, _________________________________________
________________________________________________________________
________________________________________________________________
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