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Inferential Statistics
Published in Aliakbar Montazer Haghighi, Indika Wickramasinghe, Probability, Statistics, and Stochastic Processes for Engineers and Scientists, 2020
Aliakbar Montazer Haghighi, Indika Wickramasinghe
Since the central limit theorem assures us that the sample mean X¯ is approximately normally distributed, that is, X¯~N(μ,σ2/n), X¯±Zα2(σn) is a CI for μ with a confidence level of ~ 100(1−α)%.
Estimation and inference
Published in Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke, Statistics in Engineering, 2019
Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke
In this context the normal distribution is referred to as the sampling distribution because it describes the probability distribution of X¯ in imagined repeated sampling. The normal distribution is an approximation, unless the distribution of {Xi} is itself normal when it is exact, but the approximation improves rapidly as the sample size increases. The distribution of {Xi}, which represents the population, is known as the parent distribution. The normal approximation for the sampling distribution of X¯ is generally good for any parent distribution with finite variance if the sample size n exceeds around 30. In practice, the approximation is commonly used for any n unless the parent distribution is thought to be substantially different from a normal distribution (see Exercise 7.44). The higher the confidence level, the wider is the confidence interval. For a given confidence level, the confidence interval becomes narrower as the sample size increases.
Confidence Intervals
Published in Lawrence S. Aft, Fundamentals of Industrial Quality Control, 2018
In addition to stating the point estimate, it is often desirable to establish an interval within which the true population parameter may be expected with a certain degree of confidence to fall. For example, after measuring the tensile strength of steel rods, one might say that the best estimate of the average tensile strength is 732; the true mean is between 725 and 739. (If more confidence were desired for the same data, a wider interval would be specified. A 95 percent confidence interval would be even wider — for example, between 722.49 and 741.51.) A confidence interval is a range of values that has a specified likelihood of including the true value of a population parameter. It is calculated from sample calculations of the parameters.
Cross-sectional community-based study to assess the awareness of toxoplasmosis in Saudi Arabia
Published in International Journal of Environmental Health Research, 2023
Hanadi B. Baghdadi, Ibrahim Abbas, Mohamed Abdo Rizk
This community-based cross-sectional study was conducted between December 2022 and January 2023. A structured questionnaire was designed electronically to evaluate knowledge of Saudi population in the Eastern province (Sharqiyah) on toxoplasmosis. Sharqiyah is the largest Saudi province geographically and consists of 13 governorates (Figure 1). About 5 million people live in this province, which ranks third in terms of population in Saudi Arabia overall (15.0%). The province shares a border with some nearby countries to Saudi Arabia including Bahrain, Qatar, Oman and the United Arab Emirates. Approximately two-thirds of Sharqiyah is desert, and a few areas have become important sites for desert farming in the context of the green revolution in farming in the country. The province is also a home for the main oil and gas fields in Saudi Arabia. Sample size of people participated in the study was calculated depending on the equation mentioned by (Charan and Biswas 2013) which is stated as: Sample size=(Z-score)2 X StD X (1- STD)/(Confidence interval)2. Where, Z score indicates Zeta-score that depends on confidence level for conducting the current research.
Artificial Intelligence Aided Agricultural Sensors for Plant Frostbite Protection
Published in Applied Artificial Intelligence, 2022
Shiva Hassanjani Roshan, Javad Kazemitabar, Ghorban Kheradmandian
In inferential statistics, statistical hypothesis testing is one of the most important and conventional methods. This test has been used in this study to guarantee the quality of the experiment results. Tor this purpose, the values for p-value and T-value are calculated. Null-hypothesis is usually an opinion about the parameter or the statistical population which had already existed and our goal is to reject the null hypothesis. Rejecting null-hypothesis means that our findings were statistically meaningful. The accuracy or error rate of voting for the rejection of null-hypothesis is called significance level which was assigned to 95% in this study. The significance level shows how much the maximum error was while rejecting the null-hypothesis. In addition to the parameters above, confidence interval, degree of freedom, and the mean are also obtained for the target variable. The confidence interval is a kind of interval estimation and shows the amount of confidence in the existence of a parameter in an interval or boundary of the studied population. The degree of freedom shows how much power of choice exists.
Identifying DMSMS availability risk at the system level
Published in International Journal of Production Research, 2021
James K. Starling, Youngjun Choe, Christina Mastrangelo
The results from the first scenario provide an analyst the ability to compare relative availability risk for two configuration parts with differing rates of churn (for homogeneous vendor parts). As expected, the configuration part with a greater churn rate exhibits higher availability risk and risk variability, both in terms of , Figure 5(a), and , Figure 5(b). Table 3 provides point estimates for the mean and median with 95% confidence intervals for availability risk. The Tukey HSD test indicates there is a difference between the means of CP 1 and CP 2 at the significance level for both models. The confidence intervals presented are individual and calculated using the central limit theorem.