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, _ ______________________________

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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, _________________________________________
________________________________________________________________
________________________________________________________________

2. SWIMMER'S FLEXIBILITY STUDY
Some statietica
Before:
mean = 19.4160; median = 18. 4€
mean = 18.8433: median = 18.BE
After:
Let difference = before - after
d = 0.5727
m, = 0.95
data: before
* = 0.92695
pvalue o.2456
Wilk-Shapiro Test for Normality
data: after
* = 0.97168
Pvalue = 0.21
data:
difference
* = 0.96992
pvalue = 0.0569
Ha: not equal to 0
*- 1.719
p-valu
Student'a teat on Paired Samplea: Before va After
Ha: less than 0
-- 1.719
Pvalue = o.951
Ha: greater than 0
-1.7819
- 0.09646
pvalu
- 0.04023
Ha: not equal to 0
V - 19.5
pvalue - O.09947
Wilcoxon Matched-Paire Signed Ranka Teat: Before ve After
Ha: less than o
V - 9.5
2value 0.955
Ha: greater than 0
V - i9.5
L2value - 0.04974
Fteet for Equality of Veriancee
F = 1.1255
p-value 0.e28
Student's tteet on Two Independent Pop'n Meane: Before ve After
Ha: not equal so 0
*-0.58311
pvalue o.5645
Ha: les than 0
*- 0.5311
Ha: greater than 0
: - 0.5311
pvalue = o.2822
Pvalue = o.7178
Welch's t-teat on Two Independent Pop'n Meane: Before va After
Ha: not egual to 0
*- 0.58311
p-value = o.5645
Ha: less than 0
* - 0.5311
p-value = 0.7177
Ha: greater than 0
* = 0.58311
pvalue = C.2023
Mann-Whitney Test on Two Independent Pop'n Means: Before vs After
Ha: not equal to 0
* = 120
p-value =0.7748
Ha: greate: than 0
* = 120
p-value = 0.3874
Ha: less than 0
* = 120
p-value = 0. 6281

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