- 7.4.42: Determine the values of the following quantities:a. x.1,152 b. x.1,...
- 7.4.43: Determine the following:a. The 95th percentile of the chi-squared d...
- 7.4.44: The amount of lateral expansion (mils) was determinedfor a sample o...
- 7.4.45: Wire electrical-discharge machining (WEDM) is a processused to manu...
- 7.4.46: The article Concrete Pressure on Formwork (Mag.of Concrete Res., 20...
Solutions for Chapter 7.4: Confidence Intervals for the Variance and Standard Deviation of a Normal Population
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
Solutions for Chapter 7.4: Confidence Intervals for the Variance and Standard Deviation of a Normal PopulationGet Full Solutions
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
The probability of an event given that the random experiment produces an outcome in another event.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Another name for a cumulative distribution function.
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
The variance of an error term or component in a model.
Estimate (or point estimate)
The numerical value of a point estimator.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .