- 3.2.1: Assume that X and Y are independent measurements with uncertainties...
- 3.2.2: A measurement of the circumference of a disk has an uncertainty of ...
- 3.2.3: The length of a rod is to be measured by a process whose uncertaint...
- 3.2.4: The volume of a cone is given by V = r 2h/3, where r is the radius ...
- 3.2.5: In the article The Worlds Longest Continued Series of Sea Level Obs...
- 3.2.6: A cylindrical hole is bored through a steel block, and a cylindrica...
- 3.2.7: A force of F = 2.2 0.1 N is applied to a block for a period of time...
- 3.2.8: The period T of a simple pendulum is given by T = 2 L/g where L is ...
- 3.2.9: The specific gravity of a substance is given by G = DS /DW , where ...
- 3.2.10: In a Couette flow, two large flat plates lie one on top of another,...
- 3.2.11: According to Newtons law of cooling, the temperature T of a body at...
- 3.2.12: In the article Influence of Crack Width on Shear Behaviour of SIFCO...
- 3.2.13: Nine independent measurements are made of the length of a rod. The ...
- 3.2.14: A certain scale has an uncertainty of 3 g and a bias of 2 g. a. A s...
- 3.2.15: The volume of a rock is measured by placing the rock in a graduated...
- 3.2.16: A student measures the spring constant k of a spring by loading it ...
- 3.2.17: A certain chemical process is run 10 times at a temperature of 65C ...
- 3.2.18: An object is weighed four times, and the results, in milligrams, ar...
- 3.2.19: The length of a component is to be estimated through repeated measu...
- 3.2.20: The lengths of two components will be measured several times. The u...
Solutions for Chapter 3.2: Linear Combinations of Measurements
Full solutions for Statistics for Engineers and Scientists | 4th Edition
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
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
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
Another term for the conidence coeficient.
A probability distribution for a continuous random variable.
Formulas used to determine the number of elements in sample spaces and events.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Discrete random variable
A random variable with a inite (or countably ininite) range.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Estimate (or point estimate)
The numerical value of a point estimator.
Exponential random variable
A series of tests in which changes are made to the system under study
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
A signal from a control chart when no assignable causes are present
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
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 .