- 5.3.1: Find the value of tn1,/2 needed to construct a twosided confidence ...
- 5.3.2: Find the value of tn1, needed to construct an upper or lower confid...
- 5.3.3: Find the level of a two-sided confidence interval that is based on ...
- 5.3.4: True or false: The Studentst distribution may be used to construct ...
- 5.3.5: The article Wind-Uplift Capacity of Residential Wood Roof-Sheathing...
- 5.3.6: The following are summary statistics for a data set. Would it be ap...
- 5.3.7: The article An Automatic Visual System for Marble Tile Classificati...
- 5.3.8: A chemist made eight independent measurements of the melting point ...
- 5.3.9: Six measurements are taken of the thickness of a piece of 18-gauge ...
- 5.3.10: Fission tracks are trails found in uranium-bearing minerals, left b...
- 5.3.11: The article Effect of Granular Subbase Thickness on Airfield Paveme...
- 5.3.12: The article Influence of Penetration Rate on Penetrometer Resistanc...
- 5.3.13: Ten samples of coal from a Northern Appalachian source had an avera...
- 5.3.14: The following MINITAB output presents a confidence interval for a p...
- 5.3.15: The following MINITAB output presents a confidence interval for a p...
- 5.3.16: The concentration of carbon monoxide (CO) in a gas sample is measur...
- 5.3.17: The article Filtration Rates of the Zebra Mussel (Dreissena polymor...
Solutions for Chapter 5.3: Small-Sample Confidence Intervals for a Population Mean
Full solutions for Statistics for Engineers and Scientists | 4th Edition
Solutions for Chapter 5.3: Small-Sample Confidence Intervals for a Population MeanGet Full Solutions
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A probability distribution for a continuous random variable.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
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.
An expression sometimes used for nonlinear regression models or polynomial regression models.
Defects-per-unit control chart
See U chart
A matrix that provides the tests that are to be conducted in an experiment.
The variance of an error term or component in a model.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
A subset of a sample space.
A property of a collection of events that indicates that their union equals the sample space.
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function