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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
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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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:
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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