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Is total area under a normal distribution finite?
Yes, and is equal to 1. This is true for normal distribution using any mean and variance.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
Does t-distribution rely on degree of freedom?
Yes. The parameters of the t distribution are mean, variance and the degree of freedom. The degree of freedom is equal to n-1, where n is the sample size. As a rule of thumb, above a sample size of 100, the degrees of freedom will be insignificant and can be ignored, by using the normal distribution. Some textbooks state that above 30, the degrees of freedom can be ignored.
Which measure of variation is appropriate when using the mean?
The variance or standard deviation.
What is the symbol to denote the sample variance?
s2, using the Roman lower case letter.
In a study using 9 samples and in which the population variance is unknown the distribution that should be used to calculate confidence intervals is?
In a study using 9 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is
What has the author Stephen F Duffy written?
Stephen F. Duffy has written: 'Analysis of whisker-toughened ceramic components' -- subject(s): Algorithms, Ceramics, Fracture strength, Whisker composites, Structural reliability 'Reliability analysis of structural ceramic components using a three-parameter Weibull distribution' -- subject(s): Weibull distribution, Ceramic materials
Is total area under a normal distribution finite?
Yes, and is equal to 1. This is true for normal distribution using any mean and variance.
Advantages of using the analysis of variance?
Explian DOE using Variance Analysis
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
When using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
Does t-distribution rely on degree of freedom?
Yes. The parameters of the t distribution are mean, variance and the degree of freedom. The degree of freedom is equal to n-1, where n is the sample size. As a rule of thumb, above a sample size of 100, the degrees of freedom will be insignificant and can be ignored, by using the normal distribution. Some textbooks state that above 30, the degrees of freedom can be ignored.
What do you mean by minimum tensile strength?
Tensile strength is determined from testing a large number of samples. Some will fail higher or lower than others, and an average strength is determined. Minimum tensile strength is usually calculated from statistics using a Weibull probability analysis. In this case the minimum tensile strength usually is reported as the Weibull A value, which is the value at which 99% will survive with 95% confidence. Weibull B, usually based on fewer samples, is the minimum value determined to survive with 90% reliability and 95 % confidence.
Which measure of variation is appropriate when using the mean?
The variance or standard deviation.
What does a favorable direct materials efficiency variance indicate?
A favorable direct materials efficiency variance indicates that you are using less material in production than was budgeted for.
What are some of the benefits of using a z-score?
Using z-scores allows for standardizing data so that different datasets can be easily compared. They also provide insight into how far a data point is from the mean, helping identify outliers. Additionally, z-scores are used to calculate probabilities and make statistical inferences.
What is the symbol to denote the sample variance?
s2, using the Roman lower case letter.
