- 5.7.1: The article Simulation of the Hot Carbonate Process for Removal of ...
- 5.7.2: The article Effect of Refrigeration on the Potassium Bitartrate Sta...
- 5.7.3: Transepidermal water loss (TEWL) is a measure of the rate that wate...
- 5.7.4: Breathing rates, in breaths per minute, were measured for a group o...
- 5.7.5: A group of five individuals with high blood pressure were given a n...
- 5.7.6: A sample of 10 diesel trucks were run both hot and cold to estimate...
- 5.7.7: For a sample of nine automobiles, the mileage (in 1000s of miles) a...
- 5.7.8: Refer to Exercise 7. Someone suggests that the paired design be rep...
- 5.7.9: A tire manufacturer is interested in testing the fuel economy for t...
- 5.7.10: Refer to Exercise 9. In a separate experiment, 18 cars were outfitt...
Solutions for Chapter 5.7: Confidence Intervals with Paired Data
Full solutions for Statistics for Engineers and Scientists | 4th Edition
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.
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.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
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 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 .
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
The response variable in regression or a designed experiment.
The amount of variability exhibited by data
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
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.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
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
In statistical quality control, that portion of a number of units or the output of a process that is defective.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.