- 3.1.1: The boiling point of water is measured four times. The results are ...
- 3.1.2: Two thermometers are calibrated by measuring the freezing point of ...
- 3.1.3: The weight of an object is given as 67.20.3 g. True or false: a. Th...
- 3.1.4: For some measuring processes, the uncertainty is approximately prop...
- 3.1.5: A person stands on a bathroom scale. The reading is 150 lb. After t...
- 3.1.6: A person gets on and off a bathroom scale four times. The four read...
- 3.1.7: In a hypothetical scenario, the National Institute of Standards and...
- 3.1.8: The Kilogram is now weighed five times on a different scale. The me...
- 3.1.9: A new and unknown weight is weighed on the same scale that was used...
- 3.1.10: The article Calibration of an FTIR Spectrometer (P. Pankratz, Stati...
- 3.1.11: The length of a rod was measured eight times. The measurements in c...
Solutions for Chapter 3.1: Measurement Error
Full solutions for Statistics for Engineers and Scientists | 4th Edition
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
The variance of the conditional probability distribution of a random variable.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
A probability distribution for a continuous random variable.
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.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
A subset of effects in a fractional factorial design that deine the aliases in the design.
Estimate (or point estimate)
The numerical value of a point estimator.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
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.
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.