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The Shapiro-Wilk test is performed to validate if the distribution of the population (i.e., the distribution of the diameter of the stated colonies grown on Petri dishes at the population level in this case), from where the random sample observations (i.e., the sampled observations of diameters) are obtained is distributed normally.

The Shapiro-Wilk test is performed to validate if the distribution of the population (i.e., the distribution of the diameter of the stated colonies grown on Petri dishes at the population level in this case), from where the random sample observations (i.e., the sampled observations of diameters) are obtained is distributed normally.

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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Diameter 38.6 39.0 35.2 34.1 32.9 42.4 37.5 52.6 45.9 60.0 29.1 47.7 61.7 41.7 43.5 50.2
SMART ← Step1 a) 6:08 PM The Shapiro-Wilk test is performed to validate if the distribution of the population (i.e., the distribution of the diameter of the stated colonies grown on Petri dishes at the population level in this case), from where the random sample observations (i.e., the sampled observations of diameters) are obtained is distributed normally. From the provided R software output of the "Shapiro-Wilk normality test", it is inferred that: Test statistic value, W = 0.95617 p - value = 0.5932 Step2 b) Ő 50% Hypotheses: The hypotheses are set up as: Ho: The distribution of the diameter of the stated colonies grown on Petri dishes is symmetric (or normally distributed) at the population level. ? √x 8
Transcribed Image Text:SMART ← Step1 a) 6:08 PM The Shapiro-Wilk test is performed to validate if the distribution of the population (i.e., the distribution of the diameter of the stated colonies grown on Petri dishes at the population level in this case), from where the random sample observations (i.e., the sampled observations of diameters) are obtained is distributed normally. From the provided R software output of the "Shapiro-Wilk normality test", it is inferred that: Test statistic value, W = 0.95617 p - value = 0.5932 Step2 b) Ő 50% Hypotheses: The hypotheses are set up as: Ho: The distribution of the diameter of the stated colonies grown on Petri dishes is symmetric (or normally distributed) at the population level. ? √x 8
SMART 7:05 PM The hypotheses are set up as: Hỏ: The distribution of the diameter of the stated colonies grown on Petri dishes is symmetric (or normally distributed) at the population level. H₁: The distribution of the diameter of the stated colonies grown on Petri dishes is not symmetric (i.e., not normally distributed) at the population level. Decision rule: The p-value: From the output, The decision rule is, for a defined significance level a, if P – value ≤ a, reject Họ. value Р 36% = ? 0.5932 10 Decision: For the given value of a = 1% = 0.01, a (= 0.01) < p — value (= 0. 5932). So Hō is failed to be rejected. Conclusion: The sample provides sufficient evidence to infer that the distribution of the diameter of the stated colonies grown on Petri dishes is normally distributed for the given significance level of 1%. 8
Transcribed Image Text:SMART 7:05 PM The hypotheses are set up as: Hỏ: The distribution of the diameter of the stated colonies grown on Petri dishes is symmetric (or normally distributed) at the population level. H₁: The distribution of the diameter of the stated colonies grown on Petri dishes is not symmetric (i.e., not normally distributed) at the population level. Decision rule: The p-value: From the output, The decision rule is, for a defined significance level a, if P – value ≤ a, reject Họ. value Р 36% = ? 0.5932 10 Decision: For the given value of a = 1% = 0.01, a (= 0.01) < p — value (= 0. 5932). So Hō is failed to be rejected. Conclusion: The sample provides sufficient evidence to infer that the distribution of the diameter of the stated colonies grown on Petri dishes is normally distributed for the given significance level of 1%. 8
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