- 4.11.1: Bottles filled by a certain machine are supposed to contain 12 oz o...
- 4.11.2: A 500-page book contains 250 sheets of paper. The thickness of the ...
- 4.11.3: A commuter encounters four traffic lights each day on her way to wo...
- 4.11.4: Among all the income-tax forms filed in a certain year, the mean ta...
- 4.11.5: Bags checked for a certain airline flight have a mean weight of 15 ...
- 4.11.6: The amount of warpage in a type of wafer used in the manufacture of...
- 4.11.7: The time spent by a customer at a checkout counter has mean 4 minut...
- 4.11.8: Drums labeled 30 L are filled with a solution from a large vat. The...
- 4.11.9: The temperature of a solution will be estimated by taking n indepen...
- 4.11.10: Among the adults in a large city, 30% have a college degree. A simp...
- 4.11.11: In a process that manufactures bearings, 90% of the bearings meet a...
- 4.11.12: A machine produces 1000 steel O-rings per day. Each ring has probab...
- 4.11.13: Radioactive mass A emits particles at a mean rate of 20 per minute,...
- 4.11.14: The concentration of particles in a suspension is 30 per mL. a. Wha...
- 4.11.15: The concentration of particles in a suspension is 50 per mL. A 5 mL...
- 4.11.16: A battery manufacturer claims that the lifetime of a certain type o...
- 4.11.17: A new process has been designed to make ceramic tiles. The goal is ...
- 4.11.18: The manufacture of a certain part requires two different machine op...
- 4.11.19: Seventy percent of rivets from vendor A meet a certain strength spe...
- 4.11.20: Radiocarbon dating: Carbon-14 is a radioactive isotope of carbon th...
Solutions for Chapter 4.11: The Central Limit Theorem
Full solutions for Statistics for Engineers and Scientists | 4th Edition
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
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.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
A distribution with two modes
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
Coeficient of determination
See R 2 .
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
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.
Formulas used to determine the number of elements in sample spaces and events.
An expression sometimes used for nonlinear regression models or polynomial regression models.
A probability distribution for a discrete random variable
The amount of variability exhibited by data
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.
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.
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.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .