Credibility Hypothesis Testing of Variance of Fuzzy Normal Distribution

2017 ◽  
pp. 193-220
Author(s):  
S. Sampath ◽  
B. Ramya
Keyword(s):  
Hypothesis Testing ◽  
Normal Distribution ◽  
Test Procedures ◽  
Rejection Region ◽  
Ratio Criterion ◽  
Expected Values ◽  
Fuzzy Normal Distribution

This paper considers the problem of developing test procedures for testing credibility hypotheses about the variance of fuzzy normal distribution assuming the expected values of the distributions mentioned under null and alternative credibility hypotheses are known and equal. The cases where the underlying hypothesis is simple and composite (one sided) are considered. Tests have been derived with the help of the membership ratio criterion. Properties possessed by the developed tests, like best credibility rejection region and uniformly best rejection region have been studied. Examples are also given to illustrate the usage of the derived tests.

X-Ray Diffraction Analysis Analyze the Error of Residual Stress by Using Mathematical Statistics

2010 ◽  
Vol 43 ◽  
pp. 687-690
Author(s):  
Ai Xin Feng ◽  
Chuan Chao Xu ◽  
Yu Peng Cao ◽  
Huai Yang Sun ◽  
Gui Fen Ni ◽  
...  
Keyword(s):  
Residual Stress ◽  
Aluminum Alloy ◽  
Statistical Analysis ◽  
Diffraction Analysis ◽  
Hypothesis Testing ◽  
Normal Distribution ◽  
X Ray Diffraction ◽  
X Ray ◽  
7050 Aluminum Alloy ◽  
Stress Error

X-ray diffraction analysis methods analyze the residual stress the same location for 50 times of 7050 aluminum alloy. And taking residual stress error for statistical analysis, through hypothesis testing and analysis of the residual stress error Square diagram, obtain X-ray diffraction the residual stress error of the 7050 aluminum alloy approximately obey normal distribution.

Testing normality

2019 ◽  
Vol 86 (12) ◽  
pp. 773-783 ◽  
Author(s):  
Katy Klauenberg ◽  
Clemens Elster
Keyword(s):  
Hypothesis Testing ◽  
Normal Distribution ◽  
Multiple Testing ◽  
Hypothesis Test ◽  
Statistical Tests ◽  
Distributional Assumption ◽  
Legal Metrology ◽  
Normality Assumption ◽  
Statistical Framework ◽  
Do So

AbstractIn metrology, the normal distribution is often taken for granted, e. g. when evaluating the result of a measurement and its uncertainty, or when establishing the equivalence of measurements in key or supplementary comparisons. The correctness of this inference and subsequent conclusions is dependent on the normality assumption, such that a validation of this assumption is essential. Hypothesis testing is the formal statistical framework to do so, and this introduction will describe how statistical tests detect violations of a distributional assumption.In the metrological context we will advise on how to select such a hypothesis test, how to set it up, how to perform it and which conclusion(s) can be drawn. In addition, we calculate the number of measurements needed to decide whether a process departs from a normal distribution and quantify how sure one is about this decision then. These aspects are illustrated for the powerful Shapiro-Wilk test and by an example in legal metrology. For this application we recommend to perform 330 measurements. Briefly we also touch upon the issues of multiple testing and rounded measurements.

scholarly journals Evaluation of Sampling Plans to Detect Cry9C Protein in Corn Flour and Meal

2004 ◽  
Vol 87 (4) ◽  
pp. 950-960 ◽  
Author(s):  
Thomas B Whitaker ◽  
Mary W Trucksess ◽  
Francis G Giesbrecht ◽  
Andrew B Slate ◽  
Francis S Thomas
Keyword(s):  
Normal Distribution ◽  
Test Procedure ◽  
Enzyme Linked Immunosorbent Assay ◽  
Sampling Variance ◽  
Regression Equations ◽  
Corn Flour ◽  
Test Procedures ◽  
Sampling Plans ◽  
Sample Test ◽  
Almost All

Abstract StarLink is a genetically modified corn that produces an insecticidal protein, Cry9C. Studies were conducted to determine the variability and Cry9C distribution among sample test results when Cry9C protein was estimated in a bulk lot of corn flour and meal. Emphasis was placed on measuring sampling and analytical variances associated with each step of the test procedure used to measure Cry9C in corn flour and meal. Two commercially available enzyme-linked immunosorbent assay kits were used: one for the determination of Cry9C protein concentration and the other for % StarLink seed. The sampling and analytical variances associated with each step of the Cry9C test procedures were determined for flour and meal. Variances were found to be functions of Cry9C concentration, and regression equations were developed to describe the relationships. Because of the larger particle size, sampling variability associated with cornmeal was about double that for corn flour. For cornmeal, the sampling variance accounted for 92.6% of the total testing variability. The observed sampling and analytical distributions were compared with the Normal distribution. In almost all comparisons, the null hypothesis that the Cry9C protein values were sampled from a Normal distribution could not be rejected at 95% confidence limits. The Normal distribution and the variance estimates were used to evaluate the performance of several Cry9C protein sampling plans for corn flour and meal. Operating characteristic curves were developed and used to demonstrate the effect of increasing sample size on reducing false positives (seller's risk) and false negatives (buyer's risk).

scholarly journals The effects of six beat kick technique training on swimming speed for the 50 meters freestyle

2018 ◽  
Vol 42 ◽  
pp. 00057
Author(s):  
Meiriani Armen
Keyword(s):  
Hypothesis Testing ◽  
Normal Distribution ◽  
Training Program ◽  
Swimming Speed ◽  
Sampling Method ◽  
Test Program ◽  
Significance Level ◽  
Speed Test ◽  
Normality Test ◽  
Post Test

Freestyle is one of the main swimming styles taught to swimmers. It has various techniques from stroke and breathing to limbs moving and coordinating. The legs moving technique Six Beat Kick is one of the techniques that could make an athlete swims faster. A quasi eksperiment research with pre-test and post-test program is aimed to recognise the impacts Six Beat Kick technique training on swimming speed for the 50 meters freestyle. This research is carried out in G-Sport Center Swimming Club in Padang city. The sampling method uses purposive sampling with 20 participants. The data are collected from swimming speed test on 50 meters freestyle. Prior the training, a pre-test is conducted. Then, the athletes must follow the training program for 14 times of training. Lastly, a post-test is performed. In addition, an analysis condition testing and a research hypothesis testing use data normality test and t-test with significance level of α 0,05. From the analysis condition testing, it could be assessed that the data follow a normal distribution with Lcounted 0,108 < Ltable 0,190. The hypothesis testing has a significant impact on swimming speed for 50 meters freestyle acknowledged from tcounted 22,19 > ttable 1,73. It can be concluded that Six Beat Kick technique training program could improve the swimming speed of meters freestyle.

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