- 8.3.29: The true average diameter of ball bearings of a certaintype is supp...
- 8.3.30: A sample of n sludge specimens is selected and the pHof each one is...
- 8.3.31: The paint used to make lines on roads must reflectenough light to b...
- 8.3.32: The relative conductivity of a semiconductor device isdetermined by...
- 8.3.33: The article The Foremans View of Quality Control(Quality Engr., 199...
- 8.3.34: The following observations are on stopping distance (ft)of a partic...
- 8.3.35: The article Uncertainty Estimation in Railway TrackLife-Cycle Cost ...
- 8.3.36: Have you ever been frustrated because you could not get acontainer ...
- 8.3.37: The accompanying data on cube compressive strength(MPa) of concrete...
- 8.3.38: A random sample of soil specimens was obtained, andthe amount of or...
- 8.3.39: Reconsider the accompanying sample data on expenseratio (%) for lar...
- 8.3.40: Polymer composite materials have gained popularitybecause they have...
- 8.3.41: A spectrophotometer used for measuring CO concentration[ppm (parts ...
Solutions for Chapter 8.3: The One-Sample t Test
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
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.
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
The joint probability distribution of two random variables.
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 density function
The probability density function of the conditional probability distribution of a continuous random variable.
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
Another term for the conidence coeficient.
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.
See Control chart.
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
The variance of an error term or component in a model.
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.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.