Provide answers to the following: 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: c. Based on the results in #1b, the appropriate test procedure to answer the objective of the researchers is a test procedure. .(parametric/non-parametric)
Provide answers to the following: 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: c. Based on the results in #1b, the appropriate test procedure to answer the objective of the researchers is a test procedure. .(parametric/non-parametric)
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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Transcribed Image Text:BUTTERFLY PROBLEM
According to studies, butterflies are known to have symmetric wings. To prove this, a biologist observed 15 butterflies and measure the length of its left and right wings.
(Use right – left in your computations)
Butterfly
1
2
4
5
6.
8
Butterfly
9.
10
11
12
13
14
15
Right
2.6
4.2
4.2
4.3
4.5
4.7
4.8
4.9
Right
5.2
5.2
5.6
5.8
6.
6.
6.7
Left
2.9
3.1
3.6
3.9
4.7
4.8
4.8
5.1
Left
5.1
5.5
5.8
5.9
6.
6.6
6.6
Provide answers to the following:
Some statistics
Let difference = right – left
d = 0.02
Right:
mean = 4.98; median = 4.9
a. The samples above are
(related/independent) samples.
Left:
mean = 4.96; median = 5.1
md = 0.1
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:
Wilk-Shapiro Test for Normality
right
W = 0.95823
p-value = 0.6617
data:
data:
left
data:
difference
W = 0.94666
W = 0.88726
p-value = 0.4734
p-value = 0.06098
Student's t-test on Paired Samples: Right vs Left
Ha: less than 0
t = 0.18615
Ho (in words):
Ha (in words):
Test Procedure:
Ha: not equal to 0
t = 0.18615
Ha: greater than 0
t = 0.18615
p-value = 0.4275
p-value:
Conclusion:
p-value = 0.855
p-value = 0.5725
Wilcoxon Matched-Pairs Signed Ranks Test: Right vs Left
Ha: not equal to 0
V = 41
Ha: greater than 0
V = 41
Ha: less than 0
c. Based on the results in #1b, the appropriate test procedure to answer the
objective of the researchers is a
test procedure.
V = 41
p-value = 0.7795
p-value = 0.3898
p-value = 0.6368
(parametric/non-parametric)
F-test for Equality of Variances
F = 0.72403
d. A point estimate of the true average difference in the length of the right and left
wing of a butterfly is
p-value = 0.5537
Student's t-test on Two Independent Pop'n Means: Right vs Left
Ha: not equal to 0
t = 0.050407
Ha: greater than 0
t = 0.050407
Ha: less than 0
e. At 5% level of significance, test if the length of the right wing is greater than the
left wing of a butterfly, on average.
t = 0.050407
p-value = 0.9602
p-value = 0.5199
p-value = 0.4801
Welch's t-test on Two Independent Pop'n Means: Right vs Left
Ho: (in symbols)
; (in words) The average length of the right wing is
Ha: not equal to 0
t = 0.050407
Ha: greater than 0
t = 0.050407
p-value =
Ha: less than 0
the average length of the left wing.
t = 0.050407
0.4801
p-value = 0.9602
Ha: (in symbols)
p-value = 0.5199
; (in words) The average length of the right wing is
Mann-Whitney Test on Two Independent Pop'n Means: Right vs Left
the average length of the left wing.
Ha: not equal to 0
W = 112
p-value = 1
Ha: less than 0
Ha: greater than 0
W = 112
p-value = 0.5166
Test Procedure:
W = 112
p-value = 0.5
Justifv vour choice of test procedure:
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